At least 39 people including a toddler were hurt when a 24-year-old Afghan man ploughed into demonstrators gathered in the city centre on Thursday, putting security back in focus before a federal election on February 23.
"There is a suspicion that the act was religiously motivated and is to be understood as an attack on the free democratic basic order," the federal prosecutor's office said in a statement.
The office said a criminal investigation by the Bavarian State Criminal Police Office was also still under way.
Earlier on Friday, Munich lead prosecutor Gabriele Tilmann said the suspect had said he deliberately drove into the participants of the demonstration.
"I'm very cautious about making hasty judgements, but based on everything we know at the moment, I would venture to speak of an Islamist motivation for the crime," Tilmann said.
Officers fired on the car after the attack, but the suspect was not hit. Tilmann said the driver subsequently said the words "Allahu akbar" ("God is greatest") and prayed in the presence of police.
The attack was carried out hours before leaders including US Vice President JD Vance and Ukrainian President Volodymyr Zelenskiy arrived in the southern city for the annual Munich Security Conference, but police said there was no link between the two events.
Tilmann said there was no evidence to suggest the suspect, identified as Farhad Noori, was affiliated with any Islamist or terrorist organisations.
She said there was no indication of accomplices, but investigators were evaluating his communications - mostly in Dari, a language spoken in Afghanistan - and items obtained during searches to ascertain whether anyone had prior knowledge of the crime or was involved.
A Munich court issued an arrest warrant against the suspect and ordered him to remain in investigative custody.
German authorities say the Afghan national arrived in Germany as an unaccompanied minor in 2016, and he was in Germany legally and had been working as a store detective.
Tilmann said Noori had used social media to present himself as a bodybuilder and athlete, and had posted religious content.
He did not have any prior convictions and had not been due for deportation, deputy police chief Christian Huber said, correcting police statements from the day before that were seized upon by conservative and far-right politicians.
That false information had been announced "in the chaos of the early hours", he said.
Immigration and security issues have dominated campaigning ahead of the election, especially after other violent incidents in recent weeks, with polls show the centre-right conservatives leading followed by the far right.
In December, six people were killed in an attack on a Christmas market in Magdeburg and in January a toddler and adult were killed in a knife attack in the Bavarian town of Aschaffenburg. Immigrants have been arrested over both attacks
Conservative Friedrich Merz, the frontrunner to be Germany's next chancellor, said security would be his top priority, while the far-right AfD, in second place in polls, focused on the suspect's legal status in Germany.
