There was no immediate claim of responsibility but Islamist militants have carried out many similar operations against police and soldiers since the army ousted President Mohamed Mursi of the Muslim Brotherhood in July after mass protests against him.
The fast-growing insurgency threatens the security of the most populous Arab nation ahead of a presidential election in May - as well as the vital tourist industry on which Egypt relies for revenue.
Two bombs, left among trees outside the university, killed the police officer and wounded five other security forces who had been guarding the facility, the ministry said.
Shortly afterwards, a third blast killed one person, four security officials said.
People screamed and ran for safety after the attacks as panic spread on the streets and on campus in an upmarket area near the zoo in Giza, a Reuters witness said. Police found a fourth bomb in the area.
"We expect trouble for the long term. How can the police protect us when they can't even protect themselves. It is not possible," said student Mohamed Abdel Aziz outside Cairo University after the explosions.
Responding to Wednesday's violence, Egypt's presidential spokesman Ahmed al-Muslimani said: "Terrorist groups want Egyptian universities to be known for chaos and bloodshed instead of for modernity and civilisation."
Video footage online showed a cloud of smoke hovering above a tree-lined roundabout. A loud blast is heard moments later.
Members of the security forces clad in black uniforms are shown moving away from the suspected site of the explosions and then advancing towards it with their weapons drawn.
Reuters could not independently verify the authenticity of the video, which was released by El-Youm el-Sabaa newspaper.
ELECTION FEARS
Bombings and shootings targeting the security forces have become commonplace in Egypt since the army deposed Mursi. The government this week put the death toll from such attacks at nearly 500 people, most of them soldiers and police.
Analysts predict that militants will escalate violence before the May 26-27 presidential election that is expected to be easily won by Abdel Fattah al-Sisi, the general who toppled Mursi.
Widely seen as Egypt's de facto leader since he deposed Mursi, Sisi enjoys backing from supporters who see him as Egypt's saviour who can end the political turmoil and bring prosperity to the country.
But he is viewed by the Islamist opposition as the mastermind of a coup that ignited the worst internal strife in Egypt's modern history.
It will be the second time Egyptians have voted in a presidential election in less than two years.
But in contrast to the 2012 vote won by Mursi, this election follows a fierce government crackdown on dissent that has included both Islamists and secular-minded democracy activists.
Thousands of Brotherhood supporters have been detained and killed in mass protests and clashes with police since Mursi was deposed. Last week more than 500 were sentenced to death in a mass hearing condemned by rights groups and Western governments.
The Brotherhood, Egypt's best organised political party until last year, has been banned, driven underground and declared a terrorist group by the government.
The movement says it is committed to peaceful activism. Senior Brotherhood politician Amr Darrag condemned the violence at Cairo University on his Twitter site and said it showed the clear failure of the security forces to protect Egyptians.
Tackling Islamist insurgents based in the Sinai Peninsula will be a far more daunting task for security forces. They have shown their ability to carry out nearly daily attacks despite army offensives against strongholds.
The attacks have spread from the largely lawless Sinai to Cairo and other cities, rattling Egyptians who have longed for security since a popular uprising ousted autocrat Hosni Mubarak in 2011.
While the militants are not expected to seize power, their campaign could weaken the government by dealing a major blow to the economy. Tourism, a vital source of hard currency, has been hit hard by the bloodshed.
