The leader of Germany's governing Christian Democrats (CDU), Annegret Kramp-Karrenbauer, will not run to succeed Chancellor Angela Merkel, in a surprise announcement that scraps plans for a smooth handover of power after Merkel finishes her current term.

A scandal involving the far right in the state of Thuringia appeared to be the last straw for Kramp-Karrenbauer, who told the party leadership in Berlin that she would also quit as CDU leader, a party spokesman said on Monday.

The 57-year-old, who has progressed from local politics in the small southern state of Saarland to take on a leading role at national level, had been tipped for the top job of chancellor even before she was elected CDU leader in 2018 as part of Merkel's plan to gradually bow out of German politics. The next elections are expected in 2021.

However, AKK, as she is colloquially known, has since been hit by a number of scandals, not least following a vote in the state legislature of Thuringia last week, which saw members of her CDU vote alongside the far right in order to elect the head of government there.

Kramp-Karrenbauer said she plans a selection process for the chancellor candidate in the summer, before handing over the reigns as CDU leader.

Party sources told dpa that she had not informed senior CDU figures of her decision to stand down. She is expected to give further details in a press conference in the coming hours.

According to sources from the party, Kramp-Karrenbauer's shock announcement was met with a long silence from her colleagues. The sources told dpa that no one immediately threw their hat in the ring to be the leading election candidate for Germany's strongest party.

CDU deputy leader Armin Laschet, seen as a possible fit for chancellor, was not present at the meeting.

Merkel said on Monday that Kramp-Karrenbauer should still have a role in the German cabinet, sources said.

Kramp-Karrenbauer currently serves as defence minister, often seen as a tricky position due to Germany's ageing military equipment and the country's often conflicted position on foreign military intervention.

Kramp-Karrenbauer suffered her first scandal shortly after being elected head of the party in late 2018, when she made an off-colour joke about intersex toilets.

She then faced a wave of criticism after apparently calling for stricter regulation of social media after a 26-year-old YouTuber called Rezo posted an hour-long video roasting the CDU.

More recently, Kramp-Karrenbauer's attempts to boost her international credibility, including with a plan for a security zone in war-torn Syria, fell flat.

The crisis in Thuringia, which has been without a state government since October, appears to have finally toppled her, following criticism that she showed weak leadership in responding to the issue.

Kramp-Karrenbauer has also come under pressure over her refusal to work with both the far-right Alternative for Germany (AfD) and the hard-left Die Linke, which won the Thuringia vote but has struggled to form a coalition.

Working with the AfD is seen as a red line for German political parties, but many left-of-centre establishment parties have argued that Die Linke cannot be equated with the AfD, which has been accused of harbouring Nazi sympathizers and fuelling anti-Semitism.

Parties in the state continued to hold talks on Monday to find a way out of the crisis after Thomas Kemmerich, the candidate voted into office by the CDU, AfD and his pro-business Free Liberals (FDP), stepped down under immense pressure.