“The Bavarian Central Office for Extremism and Terrorism has taken over the probe because an Islamist motive is likely,” a joint statement from Bavarian state prosecutors and the state crime investigations office said.
A 24-year-old man on Friday went on a knife rampage in Würzburg, Bavaria, stabbing three women to death and leaving six other people seriously injured.
The suspect, a Somali who arrived in Germany in 2015, struck in the city centre on Friday evening, first at a household goods store before moving on to a bank.
He was cornered by bystanders, then overpowered by police after they shot him in the thigh.
Investigators found records showing that the man had been treated at a psychiatric institution, and police said he was not a known Islamist.
However the Bavarian authorities said in their statement that a number of factors made an Islamic extremist motive appear probable.
These included witness accounts that suspect cried “Allahu Akbar” (“God is greatest” in Arabic) during his killing spree.
The suspect reportedly also mentioned “jihad” from his hospital bed after he was taken into custody.
The German government has been hesitant to classify the assault as a terror attack and urged the public to wait until the investigation is complete before drawing conclusions.
Chancellor Angela Merkel said “what is certain is that the horrific act is directed at all humanity and every religion”, her spokesman Steffen Seibert tweeted on Saturday.
But the far-right AfD party in particular has seized on the violence just three months before a general election.