Witnesses said the blasts sent up a cloud of smoke and dust near the campus, the site of repeated clashes in the past few months between police and Islamist student supporters of ousted president Mohamed Morsi.
The third bomb struck close to the main gates, where police investigators and journalists had gathered, causing no casualties.
The bombings were the latest in a spate of attacks against the security forces since the army overthrew elected Islamist Mursi last July.
They came less than a week after the army chief who toppled Mursi, Abdel Fattah al-Sisi, said he was leaving the military to stand in a presidential election set for May.
A fourth bomb placed in a car parked near the university was defused, security officials said.
The interior ministry identified the slain officer as Brigadier General Tarek al-Mergawi.