Exhibit 99.1

VIROPHARMA INCORPORATED Contacts:   Robert A. Doody Assistant Director, Investor Relations Phone (610) 321-6290   Kristina M. Broadbelt (for media) Assistant Director, PR & Advocacy Phone (610) 321- 2358

VIROPHARMA RECEIVES COMPLETE RESPONSE LETTER FOR CINRYZE™

SUPPLEMENTAL BIOLOGICS LICENSE APPLICATION FOR ACUTE TREATMENT OF

HEREDITARY ANGIOEDEMA

– Company Also Granted Expansion of Prophylaxis Therapy Label to Include Patient Labeling

for Self-Administration –

EXTON, Pa., June 4, 2009 — ViroPharma Incorporated (Nasdaq: VPHM) today announced that it has received a Complete Response letter from the U.S. Food and Drug Administration (FDA) related to its supplemental Biologics License Application (sBLA) for Cinryze™ (C1 esterase inhibitor [human]) as a treatment for acute attacks of hereditary angioedema (HAE). The FDA has requested an additional clinical study, due to their opinion that the placebo controlled study submitted in support of the sBLA lacked robustness. In the Complete Response letter, the FDA cited no safety concerns related to acute treatment with Cinryze in the clinical studies.

In addition, ViroPharma announced that FDA has approved the patient labeling for Cinryze to include self-administration for routine prophylaxis, once patients are properly trained by their healthcare provider.

“Though Cinryze is already successfully preventing attacks of HAE in many patients, there remains an unmet medical need for patients suffering from acute laryngeal attacks,” said Vincent Milano, ViroPharma’s president and chief executive officer. “Despite having a statistically significant result using the most conservative intent-to-treat (ITT) analysis, the FDA feels that the data are not robust enough to support approval at this time. We intend to respond to the FDA about our plans, and we will provide an update on the second quarter financial call.”

In October 2008, Cinryze was approved as the first and only targeted therapy for routine prophylaxis against angioedema attacks. In clinical studies and in commercial use, Cinryze has been generally well-tolerated. In the controlled clinical trials of Cinryze, there were no deaths or serious adverse reactions related to Cinryze administration, or discontinuations due to treatment-emergent adverse events.

“Patients in the United States with HAE have been waiting for a safe and effective emergency treatment for a long time,” said Anthony Castaldo, president of the U.S. and International Hereditary Angioedema Association. “Cinryze as a prophylactic treatment has changed the lives of many people living with this debilitating disease; we look forward to a day when this important therapy will be approved in the acute setting.”

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Patient Labeling for Self Administration

Self-administration of Cinryze provides patients with the ability to administer Cinryze themselves, when properly trained, in the comfort of their own home. This is an important option for some patients because they may no longer need to travel to their doctor’s office – sometimes hours away – every three to four days for in-office infusions. Cinryze is administered intravenously though a small needle.

“We are pleased that the FDA has recognized the importance of self-administration for patients,” continued Milano. “Empowering patients to administer Cinryze themselves allows them greater flexibility in managing their disease.”

About Cinryze™ (C1 esterase inhibitor [human])

Cinryze is a highly purified, pasteurized and nanofiltered plasma-derived C1 esterase inhibitor product that has been approved by FDA for routine prophylaxis against angioedema attacks in adolescent and adult patients with HAE. C1 inhibitor therapy has been used acutely for more than 35 years in Europe to treat patients with C1 inhibitor deficiency.

Cinryze has been generally well tolerated. The most common adverse reactions observed have been upper respiratory infection, sinusitis, rash and headache. No drug-related serious adverse events (SAEs) have been observed in clinical trials. Severe hypersensitivity reactions may occur. Thrombotic events have occurred in patients receiving high dose off-label C1 inhibitor therapy well above the approved treatment dosage regimen. With any blood or plasma derived product, there may be a risk of transmission of infectious agents, e.g. viruses and, theoretically, the CJD agent. The risk has been reduced by screening patients for prior exposure to certain virus infections and by manufacturing steps to reduce the risk of viral transmission including pasteurization and nanofiltration.

Cinryze is for intravenous use only. A dose of 1000 Units of Cinryze can be administered every 3 or 4 days for routine prophylaxis against angioedema attacks in HAE patients. Cinryze is administered at an injection rate of 1 mL per minute.

About Hereditary Angioedema (HAE)

HAE is a rare, severely debilitating, life-threatening genetic disorder caused by a deficiency of C1 inhibitor, a human plasma protein. This condition is the result of a defect in the gene controlling the synthesis of C1 inhibitor. C1 inhibitor maintains the natural regulation of the contact, complement, and fibrinolytic systems, that when left unrestricted, can initiate or perpetuate an attack by consuming the already low levels of endogenous C1 inhibitor in HAE patients. Patients with C1 inhibitor deficiency experience recurrent, unpredictable, debilitating, and potentially life threatening attacks of inflammation affecting the larynx, abdomen, face, extremities and urogenital tract. Patients with HAE experience approximately 20 to 100 days of incapacitation per year. There are estimated to be at least 6,000 people with HAE in the United States.

For more information on HAE, visit the U.S. HAE Association’s website at: www.haea.org.

About ViroPharma Incorporated

ViroPharma Incorporated is a biopharmaceutical company dedicated to the development and commercialization of products that address serious diseases treated by physician specialists and in hospital settings. ViroPharma commercializes Vancocin^®, approved for oral administration for treatment of antibiotic-associated pseudomembranous colitis caused by Clostridium difficile and

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enterocolitis caused by Staphylococcus aureus, including methicillin-resistant strains. ViroPharma commercializes Cinryze™ (C1 esterase inhibitor [human]) for routine prophylaxis against angioedema attacks in adolescent and adult patients with hereditary angioedema (HAE), also known as C1 inhibitor deficiency (for prescribing information on ViroPharma’s commercial products, please download the package inserts at http://www.viropharma.com/Products.aspx). ViroPharma currently focuses its drug development activities in diseases including cytomegalovirus (CMV), HAE and C. difficile.

ViroPharma routinely posts information, including press releases, which may be important to investors in the investor relations and media sections of our company’s web site, www.viropharma.com. The company encourages investors to consult these sections for more information on ViroPharma and our business.

Forward-Looking Statements

Certain statements in this press release contain forward-looking statements that involve a number of risks and uncertainties. Forward-looking statements provide the Company’s current expectations or forecasts of future events. Forward-looking statements in this press release include statements regarding ViroPharma’s clinical development programs. Our actual results could differ materially from those results expressed in, or implied by, these forward-looking statements. The development and commercialization of pharmaceutical products is subject to risks and uncertainties. The Company is evaluating the complete response letter from the FDA and there can be no assurance that the Company will either amend its supplemental BLA or conduct future clinical studies with Cinryze as a treatment for acute attacks of hereditary angioedema. In the event the Company does conduct additional clinical studies, there can be no assurance that such studies will demonstrate that Cinryze successfully treats acute hereditary angioedema attacks or that the FDA will ever approve Cinryze for the acute treatment of hereditary angioedema. In addition, there can be no assurance that the FDA will not approve a competing product which has been granted orphan drug designation thereby preventing Cinryze from reaching the market for acute treatment of HAE. These factors, and other factors, including, but not limited to those described in ViroPharma’s annual report on Form 10-K and quarterly reports on Form 10-Q filed with the Securities and Exchange Commission during 2009, could cause future results to differ materially from the expectations expressed in this press release. The forward-looking statements contained in this press release may become outdated over time. ViroPharma does not assume any responsibility for updating any forward-looking statements.

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