The exchange of fire at Shiekh Zwayed city killed five militants, army spokesperson Brigadier General Mohamed Samir said in a statement.
The firing was followed by a road side bomb attack on a military convoy in the same city in late afternoon, that killed two security personnel and injured one another, police officials said.
A medical staff was later killed while trying to transfer the injured, when unknown militants opened fire on the ambulance, the officials said.
Security forces have cordoned off the area and were looking for the attackers.
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Egypt's North Sinai has witnessed many violent attacks by militants since the January, 2011, revolution that toppled the ex-president Hosni Mubarak.
The attacks targeting police and military increased after the ouster of Islamist ex-president Mohamed Morsi in 2013 by military following massive protests against his rule.
Over 700 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.