The victim, a 19-year-old senior, suffered at least two gunshot wounds and was taken to a hospital in critical condition, police spokeswoman Monique Martin said. The suspected shooter, a 17-year-old, was in custody.
The shooting stemmed from an argument the two students had over the weekend, Mitchell High School Principal John Ware said.
"He walked up to him, shot him, and made a statement to the coach that 'It's over now,' " Mr. Ware said. The student made no attempt to flee, he said.
About 75 other students were in the cafeteria for the gym class when the shooting happened.
The school was placed on lockdown and parents were notified by the district's automated phone alert system, district spokeswoman Rita Cooper said. Many parents showed up at the 1,050-student school to pick up their children.
It was the second shooting in eight days in a Memphis high school. On Feb. 4, a 16-year-old student was shot in the leg inside a classroom during an argument with another student over music. The student wasn't seriously hurt and the suspected shooter was charged.