Israel's military describes it as a "temporary measure until Lebanon's armed forces can fully implement the agreement".
The fragile ceasefire agreement concluded in November last year means that Lebanon's regular, but relatively weak, army is to deploy forces in the south, where they are to maintain peace together with international UN forces.
In turn, the Shia militia Hezbollah is to withdraw northwards, north of the Litani River and further away from Israel.
This was to take place by January 26 at the latest, but the deadline was extended at a late stage to February 18.
Even before the announcement from Israel's military, Lebanon's President Joseph Aoun warned that Israel would not fully withdraw.
"We are afraid that a complete withdrawal will not be achieved tomorrow", he said in a statement.
Despite the agreement, deadly attacks have occurred regularly in Lebanon, which Israel often claims are directed against Hezbollah or Hamas, but which according to Lebanese reports have also affected civilians.
On Monday, a drone attack was carried out against a car in the port city of Saida in southern Lebanon, which according to Israel killed a Hamas top official.
