Police have launched a "major operation" to find the suspect, who is on the run, the spokeswoman said, adding that a "wide area" had been cordoned off.
The festival was part of a series of events to celebrate the city's 650th birthday.
Solingen is a city of some 150,000 people located an equal distance from Duesseldorf and Cologne.
People had gathered in the town on Friday evening for the first day of a three-day "Festival of Diversity", according to the event's website.
The festival was set to feature music, street theatre, variety shows, and comedians in the city center and several other areas, it said.
Up to 75,000 visitors were expected to attend over the three days.
Germany has seen a series of knife attacks over the past 12 months, with Interior Minister Nancy Faeser promising to crack down on knife crime.
A police officer was killed and five people were wounded in a knife attack at a far-right rally in the city of Mannheim in late May.
AMK/PressTV