A brief police statement said Chrupalla had to be given medical treatment backstage at about 4:30 p.m. (1430 UTC) and was then taken to a hospital, but "an obvious injury was not apparent at that time."
A spokeswoman for the Ingolstadt public prosecutor's office told the Agence France-Presse (AFP) news agency that investigators were examining a possible case of bodily harm.
An AfD spokesman told the German dpa news agency late on Wednesday that Chrupalla's condition was stable and that he would be "under intensive medical surveillance overnight."
Further details on the incident were not made available.
Police launched an appeal for witnesses. It called on those who attended the AfD rally to provide photos or videos of the event.
A police spokesman said that an investigation would look into whether a third party was involved.
What happened at the rally?
A witness told the local daily Donaukurier that the AfD leader had taken a few selfies and then collapsed before being transported to the hospital.
A local AfD representative told the dpa news agency that Chrupalla had been scheduled to speak at the event but that he had gotten caught up in a crowd melee.
Later Wednesday, Andreas Aichele, a spokesman for the Upper Bavarian Police Department, said it remained unclear whether the politician had been attacked, fallen, or simply wasn't feeling well.
Aichele said authorities were not ruling anything out and that an investigation was ongoing.
Chrupalla, 48, has led the anti-immigrant party for four years.
Tens of thousands join anti-AfD rally in Munich
Tens of thousands of people attended a demonstration in Munich in opposition to the AfD.
Police estimated that about 35,000 people attended the event in the Bavarian capital.
Charlotte Knobloch, a Holocaust survivor and former president of the Central Council of Jews in Germany, warned the crowd against the rising strength of the AfD, who have surged in opinion polls across Germany over the past year.
"If, according to polls, every seventh Bavarian voter wants to vote for an extreme right-wing party on Sunday, then this is no longer a mere slip in the political establishment," Knobloch said. "It must be clear to everyone: What starts to slide today can bury our democracy under itself tomorrow."
js/sms (DPA, AFP, AP)
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