Spokane police said the man went to his wife's workplace in the Deaconess Medical Center complex and opened fire.
No one else was injured in the shooting, authorities said.
"This is an apparent domestic violence incident," Spokane police spokeswoman Monique Cotton said.
Identities and other details were not immediately available. KHQ-TV reported that the couple had two children, who were found safe.
Deaconess Medical Center is a multi-building complex next to Interstate 90 in downtown Spokane, a city of 210,000 people in eastern Washington.
The shooting happened on the seventh floor of the Rockwood Cancer Treatment Center, police said. Other people were in the office where the shooting occurred, police said. The area was immediately evacuated.
Police received a call at about 9:30 a.m. that there had been a shooting at the medical complex, and responded in force, Cotton said.
"We took the precautions we take with an active shooter situation," she said.
The husband was still alive when reached by police, but died shortly after, police said.