Police said the attacker was a Syrian citizen with residency in Sweden.
"Initial findings indicate that the suspect may have signs of mental illness and that there is not indication for a terrorist motivation," police spokeswoman Jane Berndt told the Associated Press, adding that the investigation is still ongoing.
A police statement called it an "attempted murder".
It said the man attacked two men in a supermarket and on a sidewalk in front of a nearby hotel shortly before noon, allegedly stabbing them with a knife he had stolen from the supermarket.
Both were taken to a hospital, and police said one was released after outpatient treatment.
Berlin media outlets earlier reported that the man appeared to be randomly attacking.
They reported that several passersby pounced on the attacker and overpowered him until police arrived.
Charlottenburg is a normally quiet district of the German capital.
Germany is still reeling from the deadly Christmas market attack this month in which five people were killed and more than 200 were injured in the eastern city of Magdeburg.
A Saudi doctor was arrested on murder charges.
