Lebanese Prime Minister Najib Mikati instructed the foreign ministry to submit a complaint to the UN Security Council over the raid on the coastal town of Batroun, his office said on Saturday.
The Lebanese army and UN peacekeeping force UNIFIL are both conducting investigations into the raid, Mikati's office said, adding that he had called for "expedited" results.
First reported by Lebanese sources before an Israeli military official confirmed the military's involvement, the raid was the first of its kind since the Israel-Hezbollah war erupted in September.
"A senior operative of Hezbollah, who serves as an expert in his field, was apprehended," the Israeli military official said. "The operative has been transferred to Israeli territory and is currently being investigated."
Lebanon's state-run National News agency said an "unidentified military force" carried out a "sea landing" on the shore of Batroun, south of Tripoli, at dawn on Friday.
The force "went with all its weapons and equipment to a chalet near the beach, kidnapping a Lebanese man... and sailing away into the open sea on a speedboat".
An acquaintance of the abductee identified him as a student at the state-run Maritime Sciences and Technology Institute (MARSATI) in Batroun, Lebanon's primary training college for the shipping industry.
He was taken from student housing near the institute, but was a resident of the Shiite-majority town of Qmatiyeh further south, said the acquaintance, who spoke on condition of anonymity for security concerns.
He was completing courses to become a sea captain, the source told AFP, adding that the man was in his 30s and was well known by the teaching staff at the institute.
The Christian-majority town of Batroun has been relatively sheltered from the Israel-Hezbollah war that has pummelled south Lebanon, the southern suburbs of Beirut and the eastern Bekaa Valley.
The war has killed more than 1,900 people in Lebanon, since it began on September 23, according to an AFP tally of health ministry figures, though the real number is likely higher due to data gaps.
Israel's military says 38 soldiers have been killed in the Lebanon campaign since it began ground operations on September 30.
