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.
An unknown number of gunmen killed three people at the first shisha bar, Midnight, before driving to the Arena Bar & Cafe and shooting dead another five victims, regional broadcaster Hessenschau reports.
A dark-coloured vehicle was then seen leaving the scene.
The motive for the attack is unclear, a police statement said.
Hanau, in the state of Hessen, is about 25km (15 miles) east of Frankfurt.
It comes four days after another shooting in Berlin, near a Turkish comedy show at the Tempodrom concert venue, which killed one person.