Police Chief Frank Straub says the man was a person of interest in the woman's death. She was found dead in a home Tuesday morning.
Police spokesman Tim Schwering says "what appears to be a firearm" was found next to the man's body after he was shot Tuesday afternoon.
Reporters and photographers had gathered nearby after learning police were investigating a death at the house.
Police say the Spokane County medical examiner will identify both the man and the woman.
A regional law enforcement team will investigate the man's death.