The court order required for the release of the video was issued Thursday by the Bremen local court, police said in a statement.
The video was published "as part of a public investigation in the preliminary proceedings conducted on suspicion of the dangerous bodily injury" to Magnitz, the statement said.
The CCTV footage released by police showed Magnitz being elbowed once and then falling over as the attackers fled.
Different versions of events
Magnitz said he was attacked from behind by three men with a piece of wood around 5:30 p.m. on Monday. He said the attackers continued to kick him once he had fallen down, before he blacked out. The police video, however, shows one man hitting Magnitz from behind with his elbows after which two other people run past Magnitz.
Prosecutors cast doubt on the version of events put forth by AfD politicians when they said video footage of the attack appeared to show that while the politician was attacked, most of his injuries were sustained when he hit the ground.
AfD's Meuthen supports publication
AfD co-leader Jörg Meuthen told German newspaper Die Welt on Friday that he was in favor of the video footage being published.
Meuthen said it was not a show of distrust in the police, but to confirm whether there is a contradiction in the version of events.
"According to Mr Magnitz, a construction worker [who alerted police] made the statement that [Magnitz] had been hit with a piece of wood," Meuthen told Die Welt. "The police said, 'We didn't see such an object,'" he added.
js,law/sms (AFP, dpa)