As filed with the Securities and Exchange Commission, January, 13, 2014

UNITED STATES SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE TO

TENDER OFFER STATEMENT UNDER SECTION 14(d)(1) OR 13(e)(1)

OF THE SECURITIES EXCHANGE ACT OF 1934

The Swiss Helvetia Fund, Inc.

(Name of Subject Company (Issuer))

The Swiss Helvetia Fund, Inc.

(Name of Filing Person (Offeror))

COMMON STOCK,

$0.001 PAR VALUE PER SHARE

(Title of Class of Securities)

870875101

(CUSIP Number of Class of Securities)

Rudolf Millisits Chief Executive Officer The Swiss Helvetia Fund, Inc. 1270 Avenue of the Americas, Suite 400 New York, NY 10020 (800) 794-7700 |  | With a copy to: Stuart H. Coleman, Esq. Nicole M. Runyan, Esq. Stroock & Stroock & Lavan LLP 180 Maiden Lane New York, NY 10038-4982 (212) 806-5400

(Name, address and telephone number of person authorized to receive notices and communications on behalf of the filing persons)

Calculation of Filing Fee

|  | Transaction Valuation |  |  |  | Amount of Filing Fee |  |
|  | $66,494,050(a) |  |  |  | $8,564.43(b) |  |

(a) | Estimated for purposes of calculating the amount of the filing fee only. Pursuant to Rule 0-11(b)(1) under the Securities Exchange Act of 1934, as amended, the Transaction Value was calculated by multiplying 4,579,480 shares of common stock of the Fund (approximately 15% of the total number of shares outstanding on January 6, 2014) by $14.52 (95% of the net asset value per share of $15.28 as of the close of regular trading on the New York Stock Exchange on January 6, 2014).

(b) | Calculated at $128.80 per $1,000,000 of the Transaction Valuation.

¨ | Check the box if any part of the fee is offset as provided by Rule 0-11(a)(2) and identify the filing with which the offsetting fee was previously paid. Identify the previous filing by registration statement number, or the Form of Schedule and the date of its filing.

Amount Previously Paid: |  | Filing Party:
Form or Registration No.: |  | Date Filed:

¨ | Check the box if the filing relates solely to preliminary communications made before commencement of a tender offer.

| Check the appropriate boxes below to designate any transactions to which the statement relates:

| ¨ | third-party tender offer subject to Rule 14d-1.

| x | issuer tender offer subject to Rule 13e-4.

| ¨ | going-private transaction subject to Rule 13e-3.

| ¨ | amendment to Schedule 13D under Rule 13d-2.

Check the following box if the filing is a final amendment reporting the results of the tender offer: ¨

If applicable, check the appropriate box(es) below to designate the appropriate rule provision(s) relied upon:

| ¨ | Rule 13e-4(i) (Cross-Border Issuer Tender Offer)

| ¨ | Rule 14d-1(d) (Cross-Border Third-Party Tender Offer)

Introductory Statement

This Issuer Tender Offer Statement on Schedule TO relates to the offer by The Swiss Helvetia Fund Inc., a closed-end management investment company organized under the laws of the state of Delaware (the “Fund”), to purchase up to 4,579,480 of its issued and outstanding shares of common stock, par value $0.001 per share, at a price equal to 95% of the net asset value (“NAV”) per share, determined as of the close of the regular trading session of the New York Stock Exchange (the “NYSE”), on the business day immediately following the day the offer expires, to the seller in cash, less any applicable withholding taxes and without interest. The Fund’s offer is being made upon the terms and subject to the conditions set forth in the Offer to Purchase, dated January 13, 2014, and the related Letter of Transmittal, copies of which are attached to this Schedule TO as Exhibits (a)(1)(i) and (a)(1)(ii), respectively (which together, as amended or supplemented from time to time, constitute the “Offer”). This Issuer Tender Offer Statement on Schedule TO is intended to satisfy the reporting requirements of Rule 13e-4(c)(2) under the Securities Exchange Act of 1934, as amended.

Items 1 through 9 and Item 11.

The information in the Offer to Purchase and the related Letter of Transmittal is incorporated herein by reference with respect to Items 1 through 9 and Item 11 of this Issuer Tender Offer Statement on Schedule TO.

Item 10. Financial Statements.

Not applicable.

Item 12. Exhibits.

See Exhibit Index immediately following the signature page.

Item 13. Information Required by Schedule 13E-3.

Not applicable.

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SIGNATURE

After due inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

THE SWISS HELVETIA FUND, INC.
By: |  | /s/ Rudolf Millisits
|  | Name: Rudolf Millisits
|  | Title: Chief Executive Officer

Dated: January 13, 2014

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Exhibit Index

(a)(1)(i) |  | Offer to Purchase, dated January 13, 2014.
(a)(1)(ii) |  | Form of Letter of Transmittal (Including IRS Form W-9 and the instructions included therewith).
(a)(1)(iii) |  | Form of Letter to Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees.
(a)(1)(iv) |  | Form of Letter to Clients for use by Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees.
(a)(1)(v) |  | Letter to Stockholders of the Fund, dated January 13, 2014.
(a)(2) |  | Not applicable.
(a)(5)(i) |  | Press Release issued by the Fund, dated December 3, 2013.
(a)(5)(ii) |  | Press Release issued by the Fund, dated January 13, 2014.
(b) |  | Not applicable.
(d) |  | Not applicable.
(g) |  | Not applicable.
(h) |  | Not applicable.

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