The man, who was identified as Ahmed Hussein, 34, an employee at the university, attacked his colleague Nourhan Hussein, 32, inside the archaeology department in which she worked.
He then fled the scene and a manhunt was launched. He was found on Wednesday evening in the coastal city of Alamein.
Forensics tests later confirmed the same weapon had been used in both incidents.
Ms Hussein had filed numerous complaints about Mr Hussein to police, after repeated threats and intimidation.
Ms Hussein’s murder took place a day after another young woman was shot dead on a busy street in the Heliopolis district of Cairo.
Police determined that her killer was her former fiance, whose repeated appeals for reconciliation had been rejected.