The controversy occurred in the eastern German state, Thuringia, when Bodo Ramelow, the leader of the state, was toppled by a political collaboration which drew together the far-right AfD and Ms Merkel’s party, the CDU. Mr Ramelow’s Die Linke party was victorious in Thuringia’s state elections last year, and the party recently agreed to a coalition deal. However, in a shock political manoeuvre, Mr Ramelow then lost the vote for state premier as the AfD backed another candidate.
It was widely expected Mr Ramelow would be re-elected with ease to form a minority government in the third round of voting.
Instead, underdog candidate Thomas Kemmerich of the Free Democratic Party clinched a small victory of 45 votes to 44.
Mr Kemmerich immediately accepted his mandate to govern.
The issue causes particular difficulty for the German chancellor, as it is considered to be taboo to collaborate with the nativist AfD.
The election of Mr Kemmerich at the hands of the AfD serves as the first time since World War II that the far-right helped to elect a state premier.
After hours of speculation, the headquarters of the CDU, in Berlin, has said it refuses to be a part of any government in Thuringia.
CDU party chief, Annegret Kramp-Karrenbauer said local CDU politicians acted directly “against her will” in backing Mr Kemmerich, and the party chief vowed to push for snap elections to resolve the matter.
The FDP only scraped into local government with five seats in October, so the success of Mr Kemmerich came as a bolt from the blue.
However, political critics have pointed out Mr Kemmerich is unlikely to last long in the top job.
It is very unlikely the FDP leader would be able to formulate a cabinet, nor a majority for legislation going forward.
Tom Nuttall, the Berlin bureau chief of the Economist, described the controversy as “bizarre”.
He said: “It’s a bizarre situation. The FDP has just five seats in the state parliament and cannot hope to run a government.
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“The AfD had a candidate but none of its MPs voted for him.
“The party set a trap and the CDU/FDP walked right into it.”
Mr Kemmerich is only the second FDP state premier in German history.
Following the result, which some directly attribute to AfD support, Mr Kemmerich told the local parliament he was totally against fascism.
But local reports have suggested he was heckled with shouts of “charlatan” and “hypocrite” as he spoke.
The AfD party is strictly anti-immigration and serves as the biggest opposition force in Germany’s national parliament.
A court ruled last year that AfD state leader, Bjorn Hocke, could be described as a fascist, as the designation “rests on verifiable fact”.
Mr Kemmerich insisted he was “anti-AfD and anti-Hocke”, but unease remains locally.
Brexit co-ordinator Guy Verhofstadt weighed into the debate on social media.
The MEP tweeted side-by-side images of AfD state leader Bjorn Hocke, and Adolf Hitler.
The images were accompanied by the caption: “What happened in Thuringen is totally unacceptable. My response? Not in our name!”
Mr Verhofstadt was joined in his opinion by other Germans who also tweeted their outrage.
Armin Ganguly said: “Disgraceful what Thuringen has done. I feel deeply ashamed of Deutschland, my birth country. Germany has nothing learnt from history!”
Julian said: “Had a brief hope this morning that I only dreamed that a democrat could be elected by fascists.”
And Dr Theodor Yemenis described the election result as “the dark ghosts of history again over Germany”.
Mr Verhofstadt’s tweet appears to be an allusion to the fact the region was one of the first conduits for the emergence of Hitler’s Nazi Party.