An Israeli drone fell in the Hezbollah-dominated southern suburbs of Beirut and a second one exploded near the ground early on Sunday, a Hezbollah official told Reuters, in the first such incident in more than a decade.
The Israeli military said it does not comment on foreign reports.
The second drone caused some damage when it crashed before dawn close to Hezbollah's media centre in the Dahiyeh suburbs of Lebanon's capital Beirut, the Hezbollah official said.
It came hours after the Israeli military said its aircraft had struck Iranian forces and Shi'ite militias near Syria's capital Damascus which it said had been planning to launch "killer drones" into Israel.
Residents in Dahiyeh said they heard the sound of a blast. A witness said the army closed off the streets where a fire had started.
A Hezbollah spokesman told Lebanon's state news agency NNA the second drone was rigged with explosives causing serious damage to the media centre.
Hezbollah is now examining the first drone, he said.
Israel deems the heavily armed Shi'ite Hezbollah movement, backed by Iran, as the biggest threat across its border. They fought a month-long war in 2006 in which nearly 1,200 people, mostly civilians, died in Lebanon and 158 people died in Israel, mostly soldiers.
Lebanon has complained to the United Nations about Israeli planes regularly violating its airspace in recent years.
Israel has grown alarmed by the rising influence of its regional foe Iran during the war in neighbouring Syria, where Tehran and Hezbollah provide military help to Damascus.
Israel says its air force has carried out hundreds of strikes in Syria against what it calls Iranian targets and arms transfers to Hezbollah.
Israeli Prime Minister Benjamin Netanyahu said the strikes in Syria on Saturday thwarted a planned Iranian attack in Israel.
Syrian state media said air defences confronted the "aggression" and the army said most of the Israeli missiles were destroyed.
Hezbollah leader Hassan Nasrallah is scheduled to give a televised speech later on Sunday.