The group also said on Sunday that it would continue such flights "in response to Zionist attacks on Lebanese sovereignty".
The Israeli army confirmed the flight. "This morning, an Iranian UAV (unmanned air vehicle) operated by the Hizb Allah terror organisation infiltrated into Israel over the western Galilee," it said in a statement.
The drone later crashed in southern Lebanon, Israeli military sources told AFP.
According to Hizb Allah's statement, "A Mirsad-1 reconnaissance plane from the Islamic Resistance (the group's armed wing) overflew airspace in northern Palestine (Israel) for the first time at 10:30am (0830 GMT) and overflew a large number of Zionist settlements up to Nahariya, before returning to base safe and sound."
Nahariya lies on the Mediterranean coast several kilometres inside Israel.
The Israeli army said the incident was "further evidence of the lack of control of the Lebanese government over activities carried out from within its territory, something which may cause harm to Lebanon and its citizens".
The military said the Jewish state "views gravely any infiltration into its sovereign territory from the air, sea or by land, and will act to ensure the security of its citizens".
Israel has warned Lebanon over
the spy plane overflight incident
Neither Lebanese police nor the UN interim force in Lebanon present in the area were able to confirm or deny the flight.
Separately, an Israeli unmanned surveillance aircraft crashed down in al-Bayyada area in Naqura near the Israeli-Lebanese borders, a Lebanese security source told Aljazeera's correspondent in Beirut.
"Some resistance fighters have taken the wreckage of the crashed aircraft," the source said.
The reason behind the crash is still unknown, added our correspondent.