Police said the driver, a man in his 30s, was arrested and there was no further danger.
Among the injured, four people are in a serious condition, mayor Massimo Mezzetti told broadcaster RaiNews24.
The driver is an Italian citizen born in Bergamo, of North African origin, and a resident of the Modena area, the mayor added.
"It seems (the driver) deliberately drove onto the sidewalk, hitting several people and crashing into a shop window. He then got out of his car and brandished a knife," Mezzetti said.
One man who tried to stop the driver suffered minor injuries, the mayor said.
A witness told RaiNews24 he heard people falling and threw himself to the ground as the car approached.
He said the driver appeared to be under the influence of alcohol or drugs although authorities have not confirmed this.
"I express my solidarity with those who were injured and their families," Prime Minister Giorgia Meloni posted on X.
"What happened in Modena is extremely serious," Meloni added.
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