One person was killed on the spot and another died after jumping off the building, state-run Xinhua news agency reported.
Two other patients in the intensive care unit died after getting transferred to a safe place, a police official said.
The identity of one person who was killed in the hospital would be confirmed through DNA test, the report said.
Police detained the 27-year-old suspect, surnamed Li from Erzhou City of Hubei Province after he admitted setting fire to the No.2 Hospital of Huangshi, state run Xinhua news agency reported.