In the first such incident in more than a decade, one drone fell and second exploded near the ground and caused some damage when it crashed before dawn close to Hezbollah's media center in the capital's Dahiyeh suburbs, a Hezbollah official told Reuters.
"The new aggression...constitutes a threat to regional stability and an attempt to push the situation towards further tension," Hariri said in a statement from his office.
The Israeli military declined to comment.
The incident took place 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.
War monitor the Syrian Observatory for Human Rights said two members of Lebanon's Hezbollah group and one Iranian were killed in the Israeli strikes around Damascus.
In Tehran, a senior Revolutionary Guards commander denied on Sunday that Iranian targets had been hit in the Israeli air strikes in Syria, the semi-official ILNA news agency reported.
Israel deems Lebanon's 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.
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 center.
Hezbollah is now examining the first drone, he said. The Lebanese army said that one Israeli drone fell and another exploded at 02:30 am local time (2330 GMT), causing only material damage.
"The army arrived immediately and cordoned off the area where the two drones fell," it said.
Hezbollah leader Sayyed Hassan Nasrallah is scheduled to give a televised speech later on Sunday.
Israel has grown alarmed by the rising influence of its regional foe Iran during the war in neighboring 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 defenses confronted the "aggression" and the army said most of the Israeli missiles were destroyed.
The United States and Iran are at odds over Tehran's nuclear program and the Gulf, with both sides trading accusations over threats to the strategic waterway's security.
Iran also has wide sway in Iraq.
Iraq's paramilitary groups on Wednesday blamed a series of recent blasts at their weapons depots and bases on the United States and Israel.
The statement from the Popular Mobilisation Forces (PMF), the grouping of Iraq's mostly Shi'ite Muslim paramilitary groups, many of which are backed by Iran, said the United States had allowed four Israeli drones to enter the region accompanying U.S. forces and carry out missions on Iraqi territory.
Netanyahu hinted on Thursday of possible Israeli involvement in attacks against Iranian-linked targets in Iraq.