They said that at around 10 p.m. (2000 GMT) a single, unidentified man attacked multiple people and that the perpetrator was still at large.
"It tears my heart apart that there was an attack on our city. I have tears in my eyes when I think of those we have lost," Solingen Mayor Tim-Oliver Kurzbach said in a statement. "I pray for all those who are still fighting for their lives."
Fatal stabbings and shootings in Germany are relatively uncommon. The police said the attack occurred at a festival to honour the town s 650th anniversary.
Solingen is in North Rhine-Westphalia state, Germany’s most populous and bordering the Netherlands.
The state’s interior minister, Herbert Reul, visited the scene, telling reporters it was a targeted attack on human life but declining to speculate on the motive.
The attack occurred at the Fronhof, the mayor’s statement said, a market square where live bands were playing.
The German government has been aiming to toughen rules on knives that can be carried in public by reducing the length allowed.
In June, a 29-year-old policeman died after being stabbed in the German city of Mannheim during an attack on a right-wing demonstration.
There was a stabbing attack on a train in 2021, injuring several.