At least five people were injured after gunmen opened fire at about 22:00 local time (21:00 GMT), police told the BBC.
Police added that they are searching for the suspects, who fled the scene and are currently at large.
The first shooting was at a bar in the city centre, while the second was in Hanau's Kesselstadt neighbourhood, according to local reports.
Police officers and helicopters are patrolling both areas.
