Filed by Nuveen AMT-Free Municipal Income Fund

pursuant to Rule 425 of the Securities Act of 1933, as amended

and deemed filed pursuant to Rule 14a-6

under the Securities and Exchange Act of 1934, as amended

Subject Companies:

Nuveen AMT-Free Municipal Income Fund

Commission File No. 811-21213

Nuveen Premier Municipal Opportunity Fund, Inc.

Commission File No. 811-06457

Nuveen Premium Income Municipal Opportunity Fund

Commission File No. 811-07792

NUVEEN CLOSED END FUNDS

IMPORTANT NOTICE:

Please exercise your right to vote as soon as possible!

Dear Shareholder:

We recently sent you proxy materials concerning important proposal(s) affecting your fund, which will be considered at a Special Meeting of Shareholders of the fund on Friday, December 14, 2012 at the offices of Nuveen Investments. This letter was sent because you held shares in the fund on the record date and we have not received your vote.

YOUR FUND’S BOARD RECOMMENDS YOU VOTE “FOR” THE PROPOSAL(S)

YOUR VOTE IS VERY IMPORTANT

VOTING NOW HELPS AVOID UNNECESSARY COMMUNICATIONS WITH SHAREHOLDERS

AND ELIMINATES PHONE CALLS

Please vote using one of the following options:

1. VOTE ONLINE

Log on to the website listed on your proxy card. Please have your proxy card in hand to access your control number (located in the box) and follow the on screen instructions.

2. VOTE BY TOUCH-TONE TELEPHONE

Call the toll free number listed on your proxy card. Please have your proxy card in hand to access your control number (located in the box) and follow the recorded instructions.

3. VOTE BY MAIL

Complete, sign and date the enclosed proxy card(s), then return them in the enclosed postage paid envelope.

The proxy materials we sent you contain important information regarding the proposal that you and other shareholders are being asked to consider. Please read the materials carefully. If you have any questions regarding the proposal(s), or need assistance with voting, you may call Computershare Fund Services, the fund’s proxy solicitor, toll free at 1-866-300-0742.

Thank you for your prompt attention to this matter. If you have already voted, we appreciate your participation.