Four boats were used in the assault by “terrorists” and 32 attackers were arrested, the military said.
The Egyptian navy frequently intercepts migrant smugglers and drug traffickers off its Mediterranean coast.
The army is also facing an Islamist insurgency in the restive Sinai Peninsula, where jihadists have stepped up attacks against police and soldiers since the overthrow of Islamist President Mohammed Morsi last year.
However, direct attacks on Egyptian naval vessels are unusual.
The group behind the latest attack has not yet been identified.
‘Air force deployed’
According to Reuters, four gunmen were killed after they opened fire at the navy vessel from a fishing boat on Wednesday.
Local media reported that the Egyptian air force had been deployed to deal with the attackers.
Those captured were being interrogated, the military said.
Egyptian Army troops backed by a helicopter gunship during a sweep through villages in Sheikh Zuweyid, northern Sinai, Egypt (November 2012) The army in Sinai is battling militants angered by the overthrow of Islamist President Mohammed Morsi
The attack came after a car bomb was found outside a fast-food restaurant in the coastal town of El-Arish, in the Sinai Peninsula, late on Tuesday.
Security officials said they were evacuating residents when the bomb exploded.
One interior ministry official, speaking to AFP, said the bomb had been detonated remotely by police in a controlled explosion, and that some people were injured by shattered glass.
“We blew up the car remotely. There was a half a tonne of explosives,” Hani Abdel Latif said.
The latest attacks come several days after Egyptian jihadist group Ansar Beit al-Maqdis pledged allegiance to Islamic State (IS) militants, who have taken control of large parts of Syria and Iraq.
Ansar Beit al-Maqdis – or Champions of Jerusalem – has been behind a string of attacks on military and police targets in its stronghold in Sinai.
A three-month state of emergency was declared there last month after 31 soldiers were killed in two separate militant attacks near El-Arish on 24 October.
In a separate development on Wednesday, Egypt’s President Abdul Fattah al-Sisi signed a new law allowing for the extradition of foreign nationals sentenced or charged in Egypt.
It is believed the law may pave the way for the release of three non-Egyptian Al-Jazeera journalists, including Australian Peter Greste, who have been held for almost a year.
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