The shooting happened at around 7am on Tuesday morning in the University hospital in the city of Ostrava, located 350 kilometres (220 miles) east of Prague.
Czech police deployed an emergency unit to a university hospital.
The apparent suspect later shot himself dead as police approached his car.
Soon after the incident, Czech police released a picture of the suspect wanted over the shooting.
The Technical University of Ostrava said on its Facebook page that “a shooter, a medium-sized man in a red jacket,” was at the hospital, that all entrances to the premises were closed and police were present.
According to local reports, at least six people were shot and several people were injured.
Officials say people have been evacuated from the hospital clinic. Police are boosting security across the country.