The patrol boat had spotted militants on the coast of Rafah and engaged them, the military's spokesman said in a statement. The boat went up in flames during an ensuing firefight.
The military said it suffered no casualties.
Militants loyal to the Islamic State in Iraq and the Levant (ISIL) group have killed scores of soldiers and policemen in the peninsula since the army's overthrow of president Mohamed Mursi in 2013, AFP reported.
They have also carried out attacks west of the Suez Canal, which separates the Sinai from the rest of Egypt.
The army said on Wednesday its troops foiled a suicide car bomb attack on a military post between Cairo and Suez.