Lebanese police said that the initial rocket fire, which no group has immediately claimed responsibility for, had come from an area near Hula, on the Lebanon-Israel border.
An Israeli military spokeswoman said the army views the attack as “serious, and considers that responsibility for it falls on the Lebanese government”.
The Lebanese army and UN peacekeepers in southern Lebanon blocked off the road leading to Hula and were searching the area, reports said.
In 2006, Israel fought a war with Hezbollah, a Shia political and armed group with widespread in southern Lebanon. About 1,200 Lebanese, mostly civilians, and 160 Israelis died in the war.
Since then, there have been few incidents of attacks between groups from either country, apart from some cases of rocket fire from smaller groups in Lebanon.
There have been four rocket attacks from Lebanon into Israel this year.