Austrian authorities confirmed on Sunday that the stabbing was inspired by Islamist extremism.
The assailant was radicalized online and had links to ISIS, according to Interior Minister Gerhard Karner.
Police are checking whether the suspect acted alone.
The incident, which was captured on video showing the attacker smiling afterward, has raised security concerns across Europe.
The attack comes two days after a 24-year-old Afghan national, another asylum seeker, was arrested in connection with a vehicular assault in Munich on Thursday.
A two-year-old girl and her 37-year-old mother were killed in the attack at a trade union demonstration in the Bavarian city, and at least 36 others were wounded.
The suspect, identified by authorities as Farhad N., was detained at the scene. He has lived in Munich since arriving as an unaccompanied minor in 2016, legally residing there despite his rejected asylum application, and having no prior convictions.
Authorities are investigating him on 36 counts of attempted murder, bodily harm and dangerous interference with road traffic. Prosecutors believe he had an Islamic extremist motive but found no links to radical networks.
