President Joachim Gauck's office said he approved on Friday the government's proposal for voting on that date.
Merkel has led Germany, which has Europe's biggest economy, since 2005.
She governed for the first four years in "grand coalition" of Germany's biggest parties, her conservative Christian Democrats and the center-left Social Democrats. In 2009, she won a majority for her preferred center-right alliance with the pro-market Free Democrats.
Merkel remains popular with voters and is favored to win another four-year term, but recent polls show a majority neither for her current coalition nor for a rival center-left alliance of the Social Democrats and Greens.