"I have been given information that it was a 60-year-old local man, probably mentally unstable," the mayor, Patrik Kuncar, told Czech television.
"We can see that, here, probably, a lone shooter struck with no warning."
The broadcaster said the attacker fired about 25 rounds at lunchtime in the Druzba, or "friendship", restaurant in a residential district of the town of Uhersky Brod, 300 km southeast of Prague.
An woman injured in the incident was admitted to hospital in the nearby town of Uherske Hradiste, a hospital spokeswoman said.
An eyewitness told the broadcaster he had seen around 10 police cars arrive and police putting on bulletproof vests.
Such shooting incidents are very rare in the Czech Republic, a central European country of 10.5 million. Uhersky Brod is a town of 17,000 in the Moravia region, near the border with Slovakia.
Interior Minister Milan Chovanec flew to the scene of the attack along with police commander Tomas Tuhy.
Prime Minister Bohuslav Sobotka said in a statement: "I am shocked by the tragic attack that happened today in Uhersky Brod. I would like to express my deepest sorrow and condolences to the families and relatives of the victims."
