The Associated Press is reporting the victim was Pierce County deputy Daniel McCartney, 34, a navy veteran and married father of three.
The deputy was the first person to arrive on scene.
It was not immediately known who shot one of the suspects, or whether the deputy managed to return fire. He leaves behind a wife and three young boys, who are four, six, and nine years old.
A manhunt for the second suspect is underway.
One of two suspects was also killed during the exchange, according to the sheriff's department.
The Pierce County Sheriff's Department posted on its Facebook page early Monday that the deputy was shot just after 11:30 p.m. Sunday during a foot chase after responding to a 911 call.
Police closed off roads in the area and conducted a manhunt in an area that includes industrial sites as well as wooded areas, asking local residents to stay indoors, but did not find the man. He was wearing a dark hooded sweatshirt and a black beanie.
The injured deputy was taken to the hospital in critical condition.
The sheriff's office asked anyone with information about the shooting to come forward, and a nearby school district canceled classes in what it described as an abundance of caution.
A legacy fund has been set up at TAPCO Credit Union for the fallen deputy's family.