The Anti-Defamation League (ADL), which campaigns against anti-Semitism, put out a statement claiming Mr Musk “made an awkward gesture … not a Nazi salute”.
A spokesman for the Centre for Political Beauty said the groups had projected the image for around an hour and that police had not intervened “since we are still not in Elon Musk’s dream state”.
The group posted a video of the stunt and photos showing the protesters projecting the image, and wrote: “There’s more to come, I promise.”
Local police had initially told German media that the picture appeared to be a fake and that they had had no reports from the plant’s security but later said they were assessing the images’ veracity.
Led By Donkeys, a Left-wing group that first attracted attention for anti-Brexit posters and mocked-up tweets by political leaders, has also projected images on Tesla’s European headquarters in Amsterdam showing his support for Mr Trump.
The Tesla factory in Germany, one of the biggest foreign investments in German manufacturing in years and the company’s only European plant, has frequently been the site of protests.
Hundreds of protesters broke through police lines to reach the gates of the factory last year in protest over expansion plans. The factory was also briefly shut by an arson attack in March.
The expansion proposals, which involve cutting down half a million trees, were opposed by a referendum of locals but have since been approved.
Tesla was contacted for comment.