The Seattle-bound flight took off from JFK International Airport in New York, but was diverted to Minneapolis so the man could be removed and taken into custody.
The passenger became unruly, then tried to open a door at the rear of the 737, Alaska spokeswoman Halley Knigge told KOMO.
She said it would not be possible for a passenger to open the door in flight because of air pressure differences inside and outside the plane.
The crew initially tried to calm the man, then decided to divert to Minneapolis. Police arrested the man after the 737 landed in Minneapolis about 9:45 a.m. local time, KOMO reported.
The plane finally landed in Seattle just before 1 p.m. local time.