The shooting came a day after 24 people were killed and more than 130 wounded when Israeli troops opened fire on protesters who breached roadblocks set up along the border.
Displaced Lebanese residents were shot by Israeli forces as they returned to southern Lebanon despite warnings that troops had yet to withdraw.
The bloodshed, which one analyst said was unlikely to re-spark war, came hours after the extension of a deadline for Israeli forces to withdraw from south Lebanon under a November ceasefire deal.
Israel on Monday began allowing thousands of Palestinians to return to the heavily destroyed north of the Gaza Strip for the first time since the early weeks of the 15-month war with Hamas, in accordance with a fragile ceasefire.
