The man killed was reportedly a farmer living in a remote area of Lebanon's eastern Beqaa region. It was not clear why he was targeted.
It follows an incursion by Syrian tanks earlier this week, raising fears that Syria's unrest is spreading.
Some 5,000 Syrians have sought refuge in Lebanon in recent months.
They include deserting soldiers and opposition members fleeing a crackdown on protesters by the Syrian government.
At least 2,900 people have died in Syria since the uprising against the rule of President Bashar al-Assad began in March.
Porous borderAccording to reports, Syrian army vehicles crossed the border near Saaba, in the Beqaa region, and attacked farmers and their homes.
Witnesses said several buildings were damaged.
A Lebanese official told AFP news agency as saying the body of the Syrian man who died was left lying at the site, and that an investigation was under way.
It is unclear why the man, named as Ali al-Khatib - who was married to a Lebanese woman and living in the area - was targeted.
The BBC's Jim Muir in Beirut says the border near the Beqaa region is porous and not even clearly defined.
Lebanon has taken in several thousand Syrians fleeing the trouble in their own country.
Lebanese Prime Minister Najib Miqati has said they are being looked after on humanitarian grounds, but our correspondent says there have been reports of activists being hunted down and sent back to Syria.