The militants attacked the ambulance, carrying a sick soldier, while it was on its way to a military hospital on el-Sheikh Zwaied's International road.
The militants, belonging to the Sinai-based militant group Ansar Beit el-Maqdes, attacked the ambulance and killed the soldier and injured the driver, officials said.
The security forces pursued the attackers killing two of them and injuring three others, they added.
North Sinai has witnessed several militant attacks since January 2011 revolution that toppled president Hosni Mubarak.
More than 500 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.