Taylor Bradford, 21, was shot Sept. 30 shortly before police found him fatally wounded in his car, which had crashed into a tree.
Memphis Police Director Larry Godwin said that the attackers intended to rob Bradford, but apparently did not get what they had come for. He declined to elaborate.
"The investigation is ongoing, and we do expect additional arrests," Godwin said.
Police said last week that one of the leads they were following was whether Bradford had won a few thousand dollars at a Mississippi casino the night before he was killed.
The three Memphis men, who are not students at the university, were identified as DaeShawn Tate, 21; Victor Trezevant, 21; and Courtney Washington, 22. All three were in police custody.
All three face the possibility of life in prison or even the death penalty, reports CBS affiliate WREG. Police are still looking for more suspects, possibly students.
After the shooting, university officials told students, faculty and staff that the suspects had fled the campus, but the school canceled classes as a precaution.
Bradford, a Nashville native who transferred to Memphis from Samford University, was buried over the weekend.