Four people received minor injuries in the attack.
About three hours after the stabbings, police arrested a man matching that description who had initially tried to evade officers.
Munich police identified the suspect, who was arrested after the incident, as a 33-year-old German citizen who was known to authorities because of past criminal acts.
The man attacked people with his knife at random, causing light injuries to eight people: a 12-year-old boy, six men and one woman, said Andrae.
"There are absolutely no indications at present of a terrorist, political or religious background, though we can only rule things out when all the questioning is finished", Andrae said.
Confirming developments, Munich police spokesman, Marcus da Gloria Martins, said: "We have arrested a person who very strongly resembles the description by witnesses, but we can not confirm that he is the attacker".
A knife-wielding man randomly attacked passersby in central Munich today, lightly injuring eight people, police said as they excluded terrorism as a motive after detaining the suspected perpetrator.
People in the area have been urged to stay indoors while the suspect is still at large.