The AfD party, which was founded in 2013, has been on the rise since 2015 amid the influx of migrants in Germany and growing terror threat in Europe.
The AfD is holding a party congress at the weekend to decide on its leadership line-up for the election, at which the party is expected to win sufficient support to enter the Bundestag lower house of parliament for the first time.
Frauke Petry, co-leader of the Alternative for Germany (AfD), said on Wednesday she would not lead the anti-immigration party's campaign for a September 24 federal election - a surprising move that could play into the hands of established parties.
However, they have sagged in recent months as the issue faded from headlines and the party became increasingly mired in infighting.
But the party has lost about a third of its supporters since late previous year, hit by a slowdown in migrant arrivals, AfD infighting and controversy over its attitude to the Nazi past.
Germany's best-known nationalist politician has called on members of Alternative for Germany to endorse her more pragmatic course instead of turning the party into a "fundamental opposition".
Petry's critics say it was she who was responsible for pulling the party to the right with incendiary rhetoric such as demanding police be allowed to shoot illegal migrants.
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"I am declaring clearly that I am available neither to stand alone as the leading candidate nor to take part in a leadership team", she said. "AfD's image has repeatedly been marked by the uncoordinated. maximum provocations of a few representatives".
Unlike far-right candidate Marine Le Pen in France, its leaders have no foreseeable chance of winning the general election in Germany, where Chancellor Angela Merkel is seeking a fourth term after almost 12 years in power.
Political commentator Albrecht von Lucke said the party's congress this weekend in Cologne, where police are bracing for up to 50,000 anti-AfD demonstrators, would be a showdown between Petry and her party rivals.
Germans are expected to vote on September 24 in a general election that will elect a new government and chancellor.
Petry, a 41-year-old chemist from the former Communist East Germany, managed to secure a two-thirds majority on the party executive board in favor of expelling Hoecke. However, the far-right wing of the AfD supports him and a party arbitration board must now decide his fate. A survey conducted by Forsa showed on Wednesday that AfD would be still able to pass the threshold of 5 percent making it eligible to enter Germany's parliament.
The shock move was widely seen as an admission of defeat, even though she stays on as the party's joint leader.
Germany's Der Spiegel magazine has reported that Petry's opponents agreed at a secret meeting last week to form a team around Gauland, a 76-year-old publicist, and 38-year-old economist Alice Weidel - who, like Petry, wants Hoecke ousted.
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