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".
According to the Deutsche Press Agency, the suspect is a 33-year-old German who has been registered in Munich.
Four people were lightly injured yesterday morning in the southern German city of Munich by a man wielding a knife who fled the scene, said police, adding possible motives were unknown.
No one was seriously hurt in the attack that started at around 8.30 a.m.in the Haidhausen area, east of downtown Munich.
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About three hours later, police arrested a man matching a description they had issued based on witness reports.
Police said they believe it was not a terror attack, they suspect instead that the assailant had psychological problems. He was wearing grey pants, a green jacket and a backpack.
Mr Andrae told reporters there is no indication that an extremist, political or religious background factored into the attack.
The police department said on Twitter that officers are looking for the assailant "with all available police forces".