Filed Pursuant to Rule 497(e)

Registration File No.: 333-230158

BLACKROCK HEALTH SCIENCES TRUST

Supplement dated March 10, 2020 to the Prospectus,

dated April 29, 2019, as supplemented to date

This supplement amends certain information in the Prospectus of BlackRock Health Sciences Trust (the “Fund”), dated April 29, 2019, as supplemented to date (the “Prospectus”). Unless otherwise indicated, all other information included in the Prospectus that is not inconsistent with the information set forth in this supplement remains unchanged. Capitalized terms not otherwise defined in this supplement have the same meanings as in the Prospectus.

Effective immediately, the following changes are made to the Prospectus:

The risk factor entitled “Risk Associated with Recent Market Events” in the subsection entitled “Item 8. Description of the Fund—Risk Factors” in Part II of the Prospectus is deleted in its entirety and replaced with the following:

Risk Associated with Recent Market Events. Stresses associated with the 2008 financial crisis in the United States and global economies peaked approximately a decade ago, but periods of unusually high volatility in the financial markets and restrictive credit conditions, sometimes limited to a particular sector or a geography, continue to recur. Some countries, including the United States, have adopted and/or are considering the adoption of more protectionist trade policies, a move away from the tighter financial industry regulations that followed the financial crisis, and/or substantially reducing corporate taxes. The exact shape of these policies is still being considered, but the equity and debt markets may react strongly to expectations of change, which could increase volatility, especially if the market’s expectations are not borne out. A rise in protectionist trade policies, and the possibility of changes to some international trade agreements, could affect the economies of many nations in ways that cannot necessarily be foreseen at the present time. In addition, geopolitical and other risks, including environmental and public health, may add to instability in world economies and markets generally. Economies and financial markets throughout the world are becoming increasingly interconnected. As a result, whether or not the Fund invests in securities of issuers located in or with significant exposure to countries experiencing economic, political and/or financial difficulties, the value and liquidity of the Fund’s investments may be negatively affected by such events.

A recent outbreak of respiratory disease caused by a novel coronavirus was first detected in China in December 2019 and has now been detected internationally. This coronavirus has resulted in closing borders, enhanced health screenings, healthcare service preparation and delivery, quarantines, cancellations, disruptions to supply chains and customer activity, as well as general concern and uncertainty. The impact of this coronavirus, and other epidemics and pandemics that may arise in the future, could affect the economies of many nations, individual companies and the market in general in ways that cannot necessarily be foreseen at the present time. In addition, the impact of infectious diseases in developing or emerging market countries may be greater due to less established health care systems. Health crises caused by the recent coronavirus outbreak may exacerbate other pre-existing political, social and economic risks in certain countries. The impact of the outbreak may be short term or may last for an extended period of time.

The following is added as the ninth paragraph to the subsection entitled “Item 8. Description of the Fund—Risk Factors—Risk of Investing in China” in Part II of the Prospectus:

From time to time and in recent months, China has experienced outbreaks of infectious illnesses and the country may be subject to other public health threats, infectious illnesses, diseases or similar issues in the future. Any spread of an infectious illness, public health threat or similar issue could reduce consumer demand or economic output, result in market closures, travel restrictions or quarantines, and generally have a significant impact on the Chinese economy, which in turn could adversely affect the Fund’s investments.

Investors should retain this supplement for future reference.