Law enforcement sources told Tacoma's KCPQ-TV the dead included a gunman and a young woman, and the wounded were two Kitsap County sheriff's deputies. The officers' wounds were not life-threatening, the TV station said.
The retail store was locked down after the 3:45 p.m. shooting and the parking lot was cordoned off with crime tape.
The Port Orchard Herald reported the relationship between the slain female, who may have been a teenager, and the dead gunman was not known.
The names of the four shooting victims had not been released.
The newspaper said Deputy Scott Wilson, a spokesman for the sheriff's office, said three deputies were dispatched to the Walmart when a shopper there reported a suspicious person at the store. The officers spotted the suspect in the parking lot and ordered him to stop. They say he turned and fired an undetermined number of shots at the deputies, who returned fire.
The man and woman were hit in the exchange, as were two of the three deputies. The male suspect died at the scene and the female died at a Tacoma hospital.
"We have no motive at this point," Wilson told the Herald. "Things here are chaotic, as you might imagine, but we have the situation under control."