The bomb, planted in Al-Bahr street near the Police Club, exploded late yesterday when an armoured police vehicle passed by it, security officials said.
At least six ambulances were rushed to the blast site, they said.
The explosion came shortly after Egyptian police and army yesterday killed 65 terrorists in the North Sinai cities of Rafah and Sheikh Zwayed.
Egypt's North Sinai has witnessed many violent attacks by militants since the January 2011 revolution that toppled ex-president Hosni Mubarak.
The military has launched security campaigns in the area, arrested suspects and demolished houses that belong to terrorists, including those facilitating tunnels leading to the Gaza Strip.