The nosedive in support for Merkel's party in Hesse, known as Hessen in Germany, was predicted by polls ahead of the crucial election.
Mrs Merkel has been CDU chairman since 2000 and has held the post of Chancellor for 13 years.
Party sources also said that Friedrich Merz, a former parliamentary leader of Merkel's conservative alliance, was ready to put himself forward for the CDU chairmanship. The state is home to 6.2 million of Germany's 82 million people. Social Democrat challenger Thorsten Schaefer-Guembel says "we are experiencing a crisis of confidence - that has a lot to do with the fact that too much waffling is going on and too little being done".
She now governs Germany in a "grand coalition" of what traditionally have been the country's biggest parties - the CDU, Bavaria's conservative Christian Social Union, and the center-left Social Democrats.
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But only the Greens, who are in opposition nationally, benefited at the polls.
In September previous year, Merkel's CDU party won the general election but more than 13% of the voting population chose the right-wing nationalists AfD, which are anti-Islam and anti-refugee.
There were gains for the Greens, who were roughly level with Social Democrats at almost 20 per cent - compared with 11.1 per cent five years ago.
The result means the anti-immigration party, which entered the federal parliament for the first time a year ago, is now also represented in all 16 German regional assemblies. In projections throughout the evening, the outgoing CDU-Green coalition was forecast to win 61 seats out of 121, securing a razor-thin majority.
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Volker Bouffier's likely re-election as state premier could make the CDU's overall losses less painful and may somewhat improve Ms. Merkel's political future after a turbulent year that inspired many to write her political obituary. The government's frailty has weakened her.
Merkel's conservatives only formed their loveless national partnership with the SPD in March after the collapse of talks on a three-way coalition of the conservatives, Greens and pro-business FDP.
Following the close election results, the SPD's leader, Andrea Nahles, has announced a mid-term review of the current coalition government next year, taking the declining voting numbers as a sign that the German electorate is growing exhausted of the coalition's constant in-fighting and lack of progress on bringing legislative change to Germany. Meanwhile, the anti-establishment Alternative for Germany has entered the last of the 16 state parliaments. It has failed to convince voters that it's achieving much on other matters.
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.
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