A passenger car drove into a street demonstration of striking workers from the Verdi trade union near the city centre and was then shot at by officers, said the deputy head of Munich police Christian Huber.
The driver, a 24-year-old Afghan asylum seeker, was arrested at the scene, Huber said.
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Earlier a fire service spokesman told AFP that several of those hurt were "seriously injured, some of them in a life-threatening condition".
The state premier of Bavaria Markus Söder told a press conference that the incident "looks like this was an attack".
The incident comes on the eve of a high-profile international conference in Munich and amid an election campaign in which immigration and security have been key issues after a spate of similar attacks.
Local media reported that the car, said to be a Mini Cooper, drove into a group of striking workers from the Verdi trade union and that ambulances had rushed to the scene.
The incident happened around 10.30am on a main road close to Munich's historic city centre.
Germany is seeing several public sector strikes at the moment as collective bargaining takes place.Â
The president of the Verdi union Frank Werneke said in a statement: "We are deeply upset and shocked at the awful incident during a peaceful demonstration by our Verdi colleagues."
The ground at the scene was littered with items including glasses, shoes, thermal blankets and a pushchair.
An eyewitness who was among the striking workers told broadcaster BR24 that he "saw a person lying under the car" after it drove into the crowd.
The latest suspected attack comes amid an already inflamed debate on immigration after several similar incidents, most recently in the Bavarian city of Aschaffenburg last month.
Two people were killed in a knife attack including a two-year-old child. After that attack a 28-year-old Afghan man was arrested whom authorities say has a history of mental illness.
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