The suspect, described as a man in his 60s, was found dead in a car near the Benjamin Moore Paint distribution centre in Vancouver, police spokeswoman Kim Kapp said.
"We do not believe there are any outstanding suspects," Kapp said. "There is no threat to the general public."
Officers said earlier they were searching for the attacker, and locked down a nearby elementary school as a precaution. A spokeswoman with Vancouver Public Schools said the Fruit Valley Community Learning Center was locked down for about 10 minutes.
No one else was injured in the shooting just before noon, Kapp said.
Police have identified both the shooter and the person he killed, but will not release their names or their relationship to each other until their families have been notified, Kapp said.
The business is in an industrial park next to a state highway. At least four police cars were at the scene hours after the shooting.
In a statement, Benjamin Moore said it was "deeply saddened" by the shooting.
"We continue to gather details of what happened, and are working with law enforcement as they conduct their investigation," said spokeswoman Kimberlee M. Bradshaw.
Vancouver is near Portland, Ore., on the north bank of the Columbia River. It's the fourth largest city in Washington, with a population of more than 161,000.
Kendra Abdich, 24, said she heard two loud bangs at about 11:30 a.m.
Abdich, who lives one block from the office park, said workers often load and unload trucks at the businesses, and sudden, loud noises aren't unusual.
But Abdich said she soon saw several police cars "flying by," and checked her computer. She saw news reports and realized she lived about 100 yards from the scene.
"It's not normal out here," Abdich said. "It's a little scary."
Associated Press writers Donna Blankinship and Phuong Le in Seattle contributed to this report.Suggest a correction