Ms Merkel has been the CDU's chairwoman since 2000 and chancellor since 2005.
Propelled by the backlash to Merkel's migration policy into the federal Bundestag a year ago, the anti-immigrant Alternative for Germany (AfD) is now represented in all 16 of Germany's state legislatures, after Hessian voters handed it a 12-percent score.
While the CDU remained the largest party in the election, which was held in the central state of Hesse, results were down 10% from the previous election.
The government has been through two major crises, first over whether to turn back small numbers of migrants at the German-Austrian border and then over what to do with the head of Germany's domestic intelligence service after he was accused of downplaying far-right violence against migrants.
Angela Merkel is to stand down as leader of her party but wants to remain as chancellor of Germany, according to reports. A very poor performance in Hesse could embolden critics to push for the Social Democrats to leave the federal coalition, and endanger the job of party leader Andrea Nahles.
Merkel's decision does not mean she will cease to be Germany's leader in December. The chancellor threw her weight behind her friend in Hesse and visited him four times on the campaign trail in recent weeks.
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But despite massive losses for the center-right CDU in Sunday's vote, the chancellor's party looks likely to cling to power in Hesse, a prosperous state that is home to Frankfurt, the financial capital.
A number of potential successors to the Merkel throne have already been named in German media, with Die Welt including leading conservative Friedrich Merz - who Merkel ousted from a party leadership position in 2002 - and CDU Secretary-General Annegret Kramp-Karrenbauer. But the CDU and ecologist Greens may lack sufficient support to renew their ruling alliance in the state.
She told party top brass her mandate running to 2021 will be "her last term", a party source said, adding that she has no plans to seek a post in the European Commission following that despite speculation to that effect in Brussels.
"The CDU faces a turning point", Mike Mohring, a regional party leader from eastern Germany, told Welt television. Nahles' comments show the SPD will put more pressure on the conservatives to deliver policy results for the center-left party. The results were quite a disappointment for the CDU candidate and Ministers-President of Hesse, Volker Bouffier, a Merkel man who has stuck with her through thick and thin.
The mass arrivals are credited with fuelling the rise of the far-right, but Merkel has resisted calls to steer the CDU further rightward in response.
The other big victor was the far-right Alternative for Germany (AfD), which entered the Hesse regional assembly for the first time with 12 percent of the vote, the ARD exit poll showed.