Prime Minister Andrej Babis told Czech public television the shooting took place around 7 a.m. in a waiting room. The attacker opened fire at people's heads from close range, Babis said.
The prime minister canceled an official visit to Estonia and was heading for the site, at the University hospital in the eastern city of Ostrava, 350 kilometers (220 miles) east of Prague.
"It's a huge tragedy," Babis later said. "It's an unfortunate, individual act."
He said the suspect had been treated in the hospital, but didn't offer details.
Interior Minister Jan Hamacek said police found the suspect's car and he shot himself in the head as they approached and died from his injuries about half an hour later. Hamacek said police will be investigating his motive.
"I'd like to assure the public that there's no danger anymore," Hamacek said.
Police identified the suspect as a 42-year-old man. Several hundred police officers had launched an extensive manhunt, using two helicopters, for the suspect and his silver-gray Renault Laguna car.
Regional police chief officer Tomas Kuzel said the suspect used an illegally held Czech-made 9 mm gun. He said police believe the suspect who had a criminal record acted alone.
Police published a photo of the suspect, having withdrawn an earlier photo of a different man. They said that man was now considered to be a witness.
Clinic director Jiri Havrlant told media the dead were four men and two women. Another man and a woman had to be operated on, while one person was more lightly wounded.
All the victims were adult patients waiting for treatment.