Peter Beuth said the perpetrator was in legal possession of arms and was a sports marksman.
The attack is being treated as an act of domestic terrorism.
German news agency dpa reported, citing unnamed security officials, that a written claim of responsibility and a video were found and are being examined by police.
Bild daily reported that some of the victims were of Kurdish descent and others are thought to have been Turkish, according to news reports from Turkey 5 of the victims are belived to be of a Turkish background.
Turkey’s foreign minister, Mevlut Cavusoglu, said the consulate in Frankfurt and the embassy in Berlin were trying to obtain information on the attack.
“According to the initial information, it was an attack with a racist motive, but we would need to wait for the [official] statement,” he told state television TRT.
At least five people have also been injured following the incidents in the German city, east of Frankfurt.
Police said the shootings took place at about 10pm local time on Wednesday.
Detectives said the Midnight shisha bar in the Heumarkt area of Hanau was targeted first, and witnesses reported hearing eight to nine gunshots.
A dark vehicle was seen fleeing the scene.
Gunshots were then heard at the Arena Bar and Cafe in the Kurt-Schumacher-Platz area, which is a short distance away. A damaged car covered in thermal foil and surrounded by shattered glass was seen near where the second shooting took place.
Hanau mayor Claus Kaminsky told Bild: “This was a terrible evening that will certainly occupy us for a long, long time and we will remember with sadness.”
The flat was then blocked off and searched by special police forces.
Earlier in the night, heavily armed officers sealed off two streets and a police helicopter was deployed.
