The plane was in the air for more than 30 minutes before it returned to Lebanese territory.
The Israeli army initially denied reports from Lebanon that Hizb Allah had succeeded in flying a drone over Western Galilee.
Israeli media described the incident as "a bold and provocative step" by Hizb Allah.
Israeli Defence Minister Shaul Mofaz said he held the Lebanese government responsible for "all security incidents emanating from within its borders".
Hizb Allah said the UAV, dubbed Mirsad-1 (Arabic for ambush) had penetrated Israel up to the town of Nahariya at 10.30am (0830 GMT) on Sunday.
In a press statement, Hizb Allah said the reconnaissance drone carried out its first flight over "occupied northern Palestine, flying over several Zionist settlements and reaching the coastal town of Nahariya before returning safely to base".
Hizb Allah has vowed more spy
planes will be sent over Israel
"This qualitative and new achievement by the Islamic Resistance in Lebanon comes as part of a natural response to the Zionist enemy's repeated and permanent violations of Lebanese airspace," said the statement.
Not the last
The statement also warned Israel that this would not be the last time drones were sent into northern Israel.
"Starting today, we will send our planes as we please," it said.
The Mirsad is a small remote-controlled drone with one engine and a small camera.
The Israeli newspaper, the Jerusalem Post, on Monday quoted an Israeli citizen of Shlomi, near the Lebanese border, as saying that he saw the small pilotless airplane.
"It looked like a small remote-controlled plane with a relatively small wingspan. I heard the plane's engine. It flew at an altitude of about 80m over our house in a southerly direction."