The bomb was planted near Rafah central hospital and went off when the army vehicle passed by it. The injured were taken to the hospital, an official said.
The official also suggested that the Sinai-based terrorist group Ansar Beit el-Maqdes may be involved in the incident.
Ansar Beit el-Maqdes, an IS affiliated group, claimed responsibility for many attack that took place in Egypt and targeted mainly police and army personnel.
Killings of security personnel by militants are frequent in North Sinai as the area has witnessed many violent attacks since the January, 2011 revolution that toppled ex-president Hosni Mubarak, who ruled for nearly three decades.
Over 600 security personnel have been reported killed since then.
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.