Egyptian Prime Minister Ibrahim Mahlab has called an emergency meeting to discuss the bombings at Cairo University.
Two bombs killed Brigadier-General Tarek El-Mergawi and injured at least five other policemen. A third bomb exploded later, but an official casualty report is yet to be released. A forth bomb was diffused.
Mahlab will meet with the ministers of interior, defence and justice, as well as the heads of general and military intelligence.
Mahlab called the dead officer, El-Mergawi, a "martyr for the nation."
He described the attacks as "cowardly" and vowed they would not hinder efforts to fight terrorism.
The authorities will continue "their efforts to build an Egypt desired by this great nation."
The bombs were either planted in or buried beneath trees. The first two bombs detonated within minutes of each other, while the third bomb went off an hour later.
Fifteen students were arrested and taken to Giza security directorate for questioning, a police source told Ahram Online.
Universities have become a key venue for protests in support of deposed president Mohamed Morsi.
Clashes have frequently broken out between pro-Morsi students and security forces since the beginning of the new semester, which was delayed for three weeks due to security concerns.
Two students died in clashes between protesters and police earlier this week at Al-Azhar University in Cairo.
In February, the interim authorities issued a decree allowing security forces to enter campuses and granting university administrators the right to expel protesting students.
Militant attacks have killed 496 people in Egypt since the ouster of president Mohamed Morsi in July 2013, according to a foreign ministry statement.
The statement said 252 police and 187 military personnel were among those killed, in addition to 57 civilians.
On 5 September, there was a failed assassination attempt on Interior Minister Mohamed Ibrahim.
On 24 December, a large explosion hit the Daqahliya security directorate in Mansoura, killing 15 and injuring over 130 policemen and civilians.
Sinai-based militant group Ansar Beit Al-Maqdis has claimed responsibility for most of the attacks.