He was then arrested for obstructing justice and was later booked into jail on first-degree murder charges, officials said.
One suspect was found dead at the scene and another is on the loose and being sought by authorities.
A Washington State trooper spotted the 34-year-old suspect just after 8 a.m. Sheriff's Department spokesman Ed Troyer identified the man as Frank William Pawul.
A woman accused of driving two suspected burglars to a Frederickson-area home where a Pierce County sheriff's deputy was killed has been arrested, according to the Sheriff's Department.
McCartney, the first deputy to arrive, became involved in a foot chase with a suspect, "during which shots were fired and the deputy was struck", the sheriff's office said. Troyer would only identify the dead suspect as a 34 or 35-year-old man.
PCSD detectives worked throughout the day to determine if the man was involved in any way with the homicide, and have developed probable cause to book him on the murder of Deputy McCartney.
The suspect's name has not been released.
A third suspect, a 52-year-old woman, was arrested early Tuesday morning for driving the getaway vehicle. In the 911 call, "dispatchers could hear screaming and a scuffle taking place", the sheriff's office said. They said it is possible that the suspect could have fled in a vehicle and is no longer in the area. Two weapons also were found at the scene, Troyer said.
Bethel School District canceled all classes for Monday out of "an abundance of caution", it reported on its Facebook page.
McCartney was a Navy veteran and served the department for three years.
"There's a sadness that will be felt and should be felt in the community", said Pierce County Sheriff Paul Pastor. He believed in what he did.
"This is another reminder that our people go out and put themselves at risk, and are too often harmed in the process", the Sheriff added.