"It appears to be a drug-induced situation," spokesman Perry Cooper said, adding the man was not armed.
He was arrested inside an American Airlines plane after a short struggle. Police said he would be booked for investigation of trespass and assault of an officer.
The plane was being checked for anything suspicious before returning to service, Cooper said.
No other airport operations were affected.
Transportation Security Administration officers chased the man initially and Port of Seattle police quickly responded.
Once the man was on the tarmac, he raced up a stairway and punched through a window in a door at the end of a jetway connecting the empty plane with the terminal, Cooper said. He crawled through the broken window glass and entered the unoccupied plane.
"He had to be tackled to the ground," the spokesman said, adding the arrested man suffered minor injuries. Cooper said officers were unhurt.