One vehicle was struck by the explosion near the Masnaa border crossing, the source told AFP on condition of anonymity.
The other vehicles in the convoy escaped the bomb attack and continued along the road, the source added.
Witnesses reported hearing an explosion in the area, and said those injured were transferred to another vehicle in the convoy and taken away.
Lebanon's National News Agency said "an explosive device detonated... On the Majdal Anjar-Masnaa road, targeting a jeep".
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Witnesses said the Lebanese army arrived in the area shortly after the blast and sealed off the scene.
The bombing is the fourth time that a vehicle has been targeted by an explosive device in the Bekaa region, which is a stronghold of the Shiite Hezbollah movement.
On July 7, three people were injured, including two Lebanese soldiers when two bombs exploded in the area.
That attack followed a similar blast on June 28, when two small bombs hit a Hezbollah convoy in the area, detonating as four cars passed, a security source said.
The conflict, pitting a Sunni-dominated rebel movement against Assad, whose Alawite faith is an offshoot of Shiite Islam, has raised sectarian tensions in Lebanon.