Two bombs targeting security posts near the university exploded in quick succession, killing Brigadier General Tarek al-Mergawi, followed by a third blast as police and journalists gathered at the scene.
Ajnad Misr (Soldiers of Egypt) said on its Facebook and Twitter accounts that it carried out the bombings in response to an "arrest campaign (targeting)... Our women and our girls".
It did not elaborate on the motive, but explained that the last bomb was detonated later than planned to avoid civilian casualties.
Ajnad Misr previously claimed one of four bombings that rocked Cairo on January 24, the day before the third anniversary of an uprising that toppled strongman Hosni Mubarak.
Those attacks killed six people.