At least five other people were wounded in the bombings and State TV named the officer as Brigadier-General Tariq al-Mirjawi, the head of the police investigation bureau.
Egypt has witnessed several attacks against government targets by militant groups following the ousting of the Muslim Brotherhood last July. Last year, the government banned the Brotherhood and last week about 525 members and supporters were sentenced to death, according to an Examiner news story.
The government says Islamists have killed almost 500 people since last summer, most of them police officers, soldiers, and intelligence officers.
There have been fears of an increase in violence in the run-up to the presidential election in May, according to observers.
Wednesday's bomb blasts occurred near a riot police unit which was posted outside of Cairo University.
Some officials suspect the bombers were university students who are either members or supporters of the radical Muslim Brotherhood.
Officials said police had been the targets of the blasts, which were reported to have been caused by improvised explosive devices.