The missile strike, late on Friday, caused substantial damage to the vessel and left four sailors missing.
Israel recovered the body of one of the four on Saturday. The ship was towed back to port in Haifa, still smouldering from the attack.
Brigadier-General Ido Nehushtan, an Israeli commander, said the body was found at sea and that the military were searching for the other three.
Nehushtan said Hezbollah had launched an Iranian-made missile at the vessel.
"This shows very profound thumbprints of Iranian involvement in Hezbollah," he said.
An Israeli military source separately said that a C802 radar-guided missile with a range of 100 kilometres had been fired at the ship as it sat off the coast, enforcing a blockade on Lebanon's ports after two Israeli soldiers were abducted on Wednesday.
"This is sophisticated weaponry," the Israeli military source said. "This is advanced weaponry that is being supplied by one terrorist state [Iran] to another."
It was thought that a second land-to-sea missile had hit and sank an Egyptian merchant ship but it has since emerged that it was a Cambodian merchant vessel that was hit.
The 12 Egyptian sailors on board survived the attack and were collected from the water by other passing ships.
Iran has denied involvement and their embassy in Beirut has released a statement saying: "These accusations by Israeli officials are baseless and constitute an attempt to escape reality and cover up the impotence of this regime in the face of resistance and the Lebanese people."
Sayyed Hassan Nasrallah, Hezbollah's leader, dramatically announced the naval attack during a live telephone call to the group's television station. The rockets were fired as he spoke.
"The surprises that I had promised you start now. Now, at sea, an Israeli warship ... off Beirut is burning and will sink," he said.
Lebanese sources say Hezbollah has more sophisticated weapons systems, most notably short-range anti-aircraft batteries that have not been used so far.
Israel believes that Hezbollah, a group backed by Iran and Syria, has between 10,000 and 12,000 rockets in its arsenal with a variety of ranges, from around 30 to 70 kilometres.
Other defence sources say Hezbollah also has longer range missiles. Asked about the claims, a source close to Hezbollah said: "Wait a few days and you'll find out."
An Israeli military official said the ship is one of the most technologically advanced in the Israeli fleet, boasting an array of Harpoon and Gabriel missiles, along with a system for electronically jamming attacking missiles and other threats.
The official, who spoke on condition of anonymity, said the missile detection and deflection system was not operating apparently because the sailors did not anticipate such an attack by Hezbollah.
The attack on the ship prompted fresh Israeli strikes on Saturday as Hezbollah answered with more rockets that hit as far as Tiberias in northern Israel -a town farther south than Haifa which was also the scene of bombings.
At least 88 people have died in Lebanon, most of them civilians, in the four-day Israeli offensive sparked by Hezbollah's capture of the two Israeli soldiers in a cross-border raid.
On the Israeli side, at least 15 have been killed - four civilians and 11 soldiers.
The violence is the fiercest since 1996 when Israel launched a 17-day attack on Hezbollah strongholds in the south, four years before its troops ended their 22-year occupation of the area.