The man burst into a restaurant around lunchtime, opening fire, according to Czech state television.
The suspect is also reported to be dead following the attack, Czech officials have said. The motive for the shooting is unclear.
Some 20 people were thought to have been in the restaurant at the time.
Although police confirmed the shooting in Uhersky Brod, about 180 miles from the capital Prague, they have yet to officially comment on the death toll.
The mayor of Uhersky Brod told Czech television that the suspect, who may have been carrying two weapons, was a local man aged around 60.
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