The man was arrested near the university's Parkinson Building on Woodhouse Lane just before 5pm yesterday.
He was wanted over a murder committed outside the West Yorkshire Police area.
The force said:
"West Yorkshire Police arrested a man during a pre-planned operation on Woodhouse Lane in the centre of Leeds. The operation was to arrest a man wanted by another force on suspicion of murder.
"The incident happened at 4.50pm when a car was stopped and the man, aged 22, was arrested on suspicion of murder. There were a number of others in the vehicle and two were given community resolution orders for possession of cannabis.
"The officers were armed and were plain clothed. No one was injured during the incident which is now at an end."