BlackRock Municipal Bond Fund, Inc.

BlackRock National Municipal Fund

(the “Fund”)

Supplement dated May 22, 2015 to the

Summary Prospectus and Prospectus dated October 28, 2014

Effective immediately, the following changes are made to the Fund’s Summary Prospectus and Prospectus, as applicable:

The third paragraph in the section of the Fund’s Summary Prospectus entitled “Principal Investment Strategies of the Fund” is deleted in its entirety and replaced with the following:

The Fund may engage in transactions in certain derivatives, such as financial futures contracts and options thereon, indexed and inverse floating rate obligations and swap agreements, including credit default swap agreements. The Fund may use derivative instruments to hedge its investments or to seek to enhance returns. The Fund may leverage its assets through the use of proceeds received through tender option bond transactions. In a tender option bond transaction, the Fund transfers municipal bonds or other municipal securities into a special purpose entity (a “TOB Trust”). A TOB Trust typically issues two classes of beneficial interests: short-term floating rate interests (“TOB Floaters”), which are sold to third party investors, and residual inverse floating rate interests (“TOB Residuals”), which are generally issued to the Fund. The Fund may invest in TOB Residuals and may also invest in TOB Floaters. The Fund will look through to the underlying municipal bond held by a TOB Trust for purposes of the Fund’s 80% policy.

The risk factor entitled “Tender Option Bonds and Related Securities Risk” in the section of the Fund’s Summary Prospectus entitled “Principal Risks of Investing in the Fund” is deleted in its entirety and replaced with the following:

Tender Option Bonds and Related Securities Risk — The Fund’s participation in tender option bond transactions may reduce the Fund’s returns and/or increase volatility. Investments in tender option bond transactions expose the Fund to counterparty risk and leverage risk. An investment in a tender option bond transaction typically will involve greater risk than an investment in a municipal fixed rate security, including the risk of loss of principal. Distributions on TOB Residuals will bear an inverse relationship to short-term municipal security interest rates. Distributions on TOB Residuals paid to the Fund will be reduced or, in the extreme, eliminated as short-term municipal interest rates rise and will increase when short-term municipal interest rates fall. TOB Residuals generally will underperform the market for fixed rate municipal securities in a rising interest rate environment. The Fund may invest in TOB Trusts on either a non-recourse or recourse basis. If the Fund invests in a TOB Trust on a recourse basis, it could suffer losses in excess of the value of its TOB Residuals.

The fourth paragraph in the section of the Fund’s Prospectus entitled “Details About the Funds—How Each Fund Invests—National Fund—Principal Investment Strategies” is deleted in its entirety and replaced with the following:

The Fund may leverage its assets through the use of proceeds received through tender option bond transactions. In a tender option bond transaction, the Fund transfers municipal bonds or other municipal securities into a special purpose entity (a “TOB Trust”). A TOB Trust typically issues two classes of beneficial interests: short-term floating rate interests (“TOB Floaters”), which are sold to third party investors, and residual inverse floating rate interests (“TOB Residuals”), which are generally issued to the Fund. The Fund may invest in TOB Residuals and may also invest in TOB Floaters. The Fund will look through to the underlying municipal bond held by a TOB Trust for purposes of the Fund’s 80% policy. TOB Trusts have historically been established by third party sponsors (e.g., banks, broker-dealers and other financial institutions). Rules implementing section 619 of the Dodd-Frank Wall Street Reform and Consumer Protection Act (the “Volcker Rule”) may preclude banking entities and their affiliates from sponsoring TOB Trusts as such Trusts have been structured prior to the effective date of the Volcker Rule. In response to these restrictions, market participants have developed a new structure for TOB Trusts designed to ensure that no banking entity is sponsoring the TOB Trust for purposes of the Volcker Rule.

The risk factor entitled “Tender Option Bonds and Related Securities Risk (National Fund Principal Risk; High Yield Fund Other Risk)” in the section of the Fund’s Prospectus entitled “Details About the Funds—Investment Risks—Principal Risks of Investing in a Fund” is deleted in its entirety and replaced with the following:

Tender Option Bonds and Related Securities Risk (National Fund Principal Risk; High Yield Fund Other Risk) — The Fund’s participation in tender option bond transactions may reduce the Fund’s returns and/or increase volatility. Investments in tender option bond transactions expose the Fund to counterparty risk and leverage risk. An investment in a tender option bond transaction typically will involve greater risk than an investment in a municipal fixed rate security, including the risk of loss of principal. Distributions on TOB Residuals will bear an inverse relationship to short-term municipal security interest rates. Distributions on TOB Residuals paid to the Fund will be reduced or, in the extreme, eliminated as short-term municipal interest rates rise and will increase when short-term municipal interest rates fall. TOB Residuals generally will underperform the market for fixed rate municipal securities in a rising interest rate environment.

The Fund may invest in TOB Trusts on either a non-recourse or recourse basis. TOB Trusts are typically supported by a liquidity facility provided by a third-party bank or other financial institution (the “Liquidity Provider”) that allows the holders of the TOB Floaters to tender their certificates in exchange for payment of par plus accrued interest on any business day, subject to the non-occurrence of tender option termination events. When the Fund invests in a TOB Trust on a non-recourse basis, and the Liquidity Provider is required to make a payment under the liquidity facility, the Liquidity Provider will typically liquidate all or a portion of the municipal securities held in the TOB Trust and then fund the balance, if any, of the amount owed under the liquidity facility over the liquidation proceeds (the “Liquidation Shortfall”).

If a Fund invests in a TOB Trust on a recourse basis, the Fund will typically enter into a reimbursement agreement with the Liquidity Provider where the Fund is required to reimburse the Liquidity Provider the amount of any Liquidation Shortfall. As a result, if the Fund invests in a TOB Trust on a recourse basis, the Fund will bear the risk of loss with respect to any Liquidation Shortfall.

To the extent that the Fund, rather than a third-party bank or financial institution, sponsors a TOB Trust, certain responsibilities that previously belonged to the sponsor bank will be performed by, or on behalf of, the Fund. The Fund’s additional duties and responsibilities under the new TOB Trust structure may give rise to certain additional risks including compliance, securities law and operational risks.

Shareholders should retain this Supplement for future reference.