The claim, in an online statement, was the first by the group for a suicide attack in Lebanon. It recently captured wide areas in northern Iraq and eastern Syria.
A suicide bomber blew himself up at a Beirut's Duroy Hotel on Wednesday when security forces raided it to arrest him. His accomplice was wounded and was being questioned at a Beirut hospital.
Lebanese officials said both men were from Saudi Arabia. Eleven people, including three security men, were wounded in the blast.
It referred to Hezbollah which is Arabic for party of God as "the party of Satan."
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"We tell the part of Satan and its army in Lebanon that this is only the beginning. Get ready for hundreds of martyrs who love the blood of Rafida," the group said, using a derogatory term for Shiite Muslims.
Previous attacks were claimed by the al-Qaida-linked group, the Abdullah Azzam Brigades, and the al-Qaida-linked Nusra Front. Both groups have warned that such attacks will continue as long as Hezbollah takes part in Syria's civil war alongside Assad's troops.