Federal prosecutors said they had taken charge of investigations into the attack - which happened late on Wednesday in Hanau, east of Frankfurt - due to indications it had an extremist motive.
Newspaper Bild said the suspected gunman had expressed far-right views in a written confession.
In shisha bars, customers share flavored tobacco from a communal hookah, or water pipe. In Western countries, they are often owned and operated by people from the Middle East or South Asia, where use of the hookah is a centuries-old tradition.
Some of those killed were of Turkish origin, a spokesman for the Turkish presidency said. "We expect German authorities to show maximum effort to enlighten this case. Racisim is a collective cancer," Ibrahim Kalin said on Twitter.
Police could not immediately be reached for comment on the Bild report.
They said earlier that said a second body was also found at the suspect's home.
"There are no indications that other suspects were involved. One of the two dead people found is highly likely the perpetrator," police said in a statement early on Thursday, adding that investigations into the identity of gunman and victims were ongoing.
Bild, Germany's biggest selling daily newspaper, said without citing a source that the suspect also left a video claiming responsibility.
Can-Luca Frisenna, whose father and brother run one of the two bars attacked, said he rushed there after learning about the shooting.
"I heard my father was affected and my little brother, they run the kiosk, I don't have much to do with it," said Frisenna. "But then I saw them both - they were horrified and they were crying and everything. So everyone was shocked."
At one of the bars on Thursday morning, forensics police in white overalls inspected the crime scene, cordoned off close to Hanau's historic market place. Nearby, traffic flowed as normal and commuters waited for buses.
Police said their information suggested the gunman had committed suicide at his home after fleeing in a car.
Bild said the suspect was a German citizen and that ammunition and gun magazines were found in the vehicle. He had a firearms hunting licence, it added.
Government spokesman Steffen Seibert tweeted: "Deep sympathy goes out to the families concerned, who are mourning the loss of their dead. With the injured, we hope they will soon recover."
Last October, an anti-Semitic gunman who denounced Jews opened fire outside a German synagogue on Yom Kippur, the holiest day of the Jewish year, and killed two people as he livestreamed his attack.