Interim Police Chief Mike Gambrell told local reporters that the shooting happened about 10:30 p.m. Monday after a man tried to enter the Greenville County Law Enforcement Center.
Gambrell said the suspect died from a self-inflicted gunshot wound.
The names of those involved have not been released. Gambrell said the officer was in serious condition after being shot twice in the side and once in the hand.
A police spokesman did not immediately return a message Tuesday morning.
Police said the suspect had fired a gun into the law enforcement center door when he found it locked. The officer who was wounded had responded to the shooting.