Washington State Patrol spokesman Keith Leary said in a phone interview that the suspect was taken into custody but declined to immediately release more details.
Seattle television station KOMO reported on Twitter that the suspect had been captured in Oak Harbor, a community about 30 miles (48 km) southwest of Burlington where the mall shooting occurred on Friday.
Television station KIRO, citing people who know the suspect, reported he is 20 years old and lives with his family in Oak Harbor, where he graduated from high school in 2015. It showed a video of police leading a young man, who did not resist, to a vehicle.
Washington state police officials said on Twitter that authorities would provide further details at a news conference.
The suspect, whose name has not been released, is believed to have entered the Cascade Mall in Burlington, around 65 miles (105 km) north of Seattle, and began shooting at about 7 p.m. local time on Friday in the cosmetics section of a Macy's department store, police said.
He initially walked into the shopping center without the rifle but surveillance video later caught him brandishing the weapon, said Lieutenant Chris Cammock of the Mount Vernon Police Department at a briefing on Saturday.
The rifle was later recovered at the mall, said Cammock, commander of the Skagit County Multi-Agency Response Team.
Four women were killed in the rampage. Later, a man who was shot, died. None of the victims were identified.
Steve Sexton, the mayor of Burlington, described the shooting as a "senseless act."
"It was the world knocking on our doorstep and it came to our little community here," he said before acknowledging the response by law enforcement. "I know now our support goes with them to bring this son of a bitch to justice."
Authorities offered no information about a possible motive for the attack, which followed a series of violent outbursts at shopping centers across the United States, including the stabbing of nine people at a Minnesota center last weekend.
"We have no indication that we have a terrorism act," said Michael Knutson, assistant special agent in charge of the Federal Bureau of Investigation's Seattle office. "I can't discount that, but I can't conclude it either."
After the shooting, police and rescue workers worked their way through the mall, clearing stores and evacuating shoppers, some of whom locked themselves in dressing rooms. The mall remained closed on Saturday as investigators sifted for evidence and attempted to recreate the crime scene.
The shooting comes less than a week after a man stabbed nine people at a mall in the central Minnesota city of St. Cloud before being shot dead by an off-duty police officer. The FBI is investigating that attack as a potential act of terrorism.