After opening fire in the store, the suspect, identified as Jarid Haddock, 21, ran across the street and fired into a vehicle, forcing the driver to move to the passenger seat. The suspect stole the car and fled, police said.
Following an hours-long manhunt, a relative of Haddock called authorities to a location behind warehouses where Haddock was hiding. Gunshots were heard while police approached and a man who identified himself as Haddock was found wounded, Murray said.
No officers were injured or used any force, he added.
Haddock died of his injuries at the scene.
Yakima is a city of about 97,000 people in Washington's Yamika Valley, an agricultural region known for apple crops and wineries.