Supporters of Germany's Social Democrats (SPD) celebrate after exit poll results were announced on public broadcaster TV ZDF during the election for a new parliament in German city-state Hamburg on Sunday in Hamburg. (Photo: AFP)

Voters handed German Chancellor Angela Merkel's conservatives their worst-ever result in Hamburg on Sunday, punishing them for flirting with the far-right in an eastern state and descending into a messy leadership battle.

Preliminary results also showed the far-right Alternative for Germany (AfD) just scraping into the Hamburg parliament, only four days after a racist gunman killed 11 people, including himself, in the western town of Hanau.

The Social Democrats (SPD) and Greens celebrated in Germany's second-biggest city after taking first and second place, meaning they will probably keep ruling together in the northern port and city-state.

The conservative Christian Democrats (CDU) suffered after party leader and Merkel protegee Annegret Kramp-Karrenbauer said she would stand aside, blowing open the race to succeed the chancellor and throwing the party into turmoil.

The CDU slipped into third place, scoring just 11.2 percent. The AfD, which has capitalized on anger over Merkel's open-door migrant policy, especially in former East Germany, won 5.3 percent, just over the five percent threshold needed to get into the state parliament, according to the preliminary results.

Kramp-Karrenbauer's move came after an eastern branch of the CDU defied the national party and voted with the AfD to install a state premier from a third party - breaking a postwar consensus among established parties of shunning the far-right.

The CDU leadership team meets on Monday and Kramp-Karrenbauer is expected to set out a timetable for a decision on the party chair and possibly the chancellor candidate. Four or five candidates are jockeying for the jobs.

Merkel, chancellor for almost 15 years, has said she will not run again in the next federal election, due by October 2021.

Preliminary results put the SPD, who share power with the conservatives at the federal level, down about six points from the last vote in 2015 but on 39.1 percent, still by far the biggest party in Hamburg.