The group's Egyptian affiliate claimed it fired a "guided missile" at the frigate north of Rafah, which neighbours the Gaza Strip, in a statement reported by the SITE Intelligence Group.
It posted three pictures showing what appeared to be a guided anti-tank missile striking the vessel and causing a large fireball.
Read: Brazen IS attacks leave more than 100 dead in Egypt
The military had earlier said one of its boats came under attack and was set on fire while pursuing militants, but that it suffered no losses.
Other navy boats rescued the crew as their vessel spewed a plume of smoke, said an AFP photographer across the border in the Gaza Strip.
https://twitter.com/erinmcunningham/status/621670226267107328
xtremists loyal to the Islamic State group have killed scores of Egyptian soldiers and policemen in the Sinai Peninsula since the army's overthrow of Islamist president Mohamed Morsi in 2013.
Read: Egypt strikes IS targets in Libya after beheadings video
The militants 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 bombing of a military post between Cairo and Suez that was claimed by the IS's affiliate in Egypt.
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