The bomb targeted a police vehicle that was carrying a group of police officers and conscripts on the Autostrad road near el-Maadi district, the statement said.
The four injured include an officer and three conscripts who were transferred to the hospital for treatment.
Egypt has witnessed several attacks since the January 2011 revolution that toppled ex-president Hosni Mubarak.
The attacks, mainly targeting the police and the military, increased after the ouster of Islamist ex-president Mohamed Morsi in 2013 by the military following massive protests against his rule.