No other injuries were reported. Identities of the victim and the shooter were not released.
KING-TV, Seattle, said the arrest was made near the school.
The shooting occurred about 7:20 a.m. as students returned to class for the first time since the holiday break. Witnesses reported hearing three shots in a school hallway shortly before the first bell.
"A friend of mine came running into the classroom saying someone had been shot and there was blood on the lockers," Cameron, a 10th grade student, told KING.
The Tacoma News Tribune reported the suspect was believed to be a Tacoma high school student but it was unclear whether he attended Foss.
Police initially locked down the school but then allowed students to leave. Those without their own transportation were taken to Wilson High School for pickup by their parents, the News Tribune said.
"I turned around and ran," Steven Stone, a 17-year-old senior, told the newspaper. "I was scared. I didn't know what else might happen."
School was canceled for the day.