The rocket was discovered by a military patrol in the area of Marjayoun in southern Lebanon, some 3 miles from the border with Israel, The Daily Star said.
Two rockets were fired toward northern Israel Wednesday night but exploded near the border near the Lebanese village Sahl al-Khiam, the newspaper said. The incident occurred as Egypt announced a cease-fire between Israel and Hamas.
A statement released by the Lebanese army said United Nations Interim Forces were investigating the incident with them.
On Monday, the army dismantled two rockets aimed at Israel in the Mazraat Halta area.
A source told the newspaper the firing of rockets from Lebanon is a solidarity attempt with Palestinians in Gaza.