Egypt has been hit by a wave of bombings and shootings since the military ousted Islamist president Mohamed Morsi in July 2013.
The five policemen, including two officers, were hurt when a bomb exploded at a small post near Helwan University in southern Cairo, security officials said.
But the interior ministry said assailants in a speeding car threw a bomb at the policemen near the university, wounding four officers and a conscript.
But militant groups have also staged attacks in other parts of the country, including Cairo.
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They say they are acting in retaliation to a brutal government crackdown targeting Morsi's supporters that has left at least 1,400 people dead since his ouster.
A militant group called Ajnad Misr (Soldiers of Egypt) claimed today's bombing on the police in a statement posted on Twitter.
"As a quick response to security forces that target university students... A group of heroes targeted the security force that besiege Helwan University," it said.
The group has claimed several previous attacks on security forces in Cairo, including one near Cairo University last month that wounded nine people.
Police have tightened security in and around universities across Egypt, where students supporting Morsi still stage regular protests.
During the past academic year, at least 14 students were killed in clashes with security forces on university campuses -- the last bastions of pro-Morsi protesters.