Egyptian military spokesman Brig Gen Mohammed Samir said the vessel caught fire in an exchange of fire with "terrorists" on the shore and that there were no fatalities among its crew members.
He did not say how much damage the vessel suffered and gave no details on the type of ship or the size of its crew.
However, security officials said an unspecified number of crew members suffered injuries from the fire and that several of them jumped overboard to escape the raging fire.
Its claim of responsibility came in a statement posted on Twitter accounts known to be linked to the group.
The authenticity of the statement could not be immediately verified, but it was accompanied by photos purporting to show what appears to be a rocket flying toward the vessel, a large explosion engulfing most of the boat and then black smoke rising up from the vessel.
A witness, fisherman Abu Ibrahim Mohammed from the neighboring Gaza Strip, said the vessel was a gunboat that was about a nautical mile off the coast when it caught fire.
Two speed boats were seen later combing the area as gunshots occasionally rang out, he added.
The vessel, according to the security officials, routinely patrols Egyptian territorial waters and has frequently been used to transport army and police personnel to mainland Egypt, the officials said.
The sea route avoids the overland journey through Sinai, where Islamic militants target government forces.
The officials spoke on condition of anonymity because they were not authorized to brief the media.
