Hezbollah said Kantar, known in Lebanon as "The Dean of Lebanese Prisoners" for spending nearly three decades in Israel, was killed along with eight others in the strike in the Damascus suburb of Jaramana last night.
Hezbollah's Al-Manar TV aired footage of what it said was the residential building targeted in Jaramana last night.
The building appeared to be completely destroyed.
Kantar was imprisoned in 1979 in Israel after he was convicted of murder in an attack that left an Israeli policeman, a father and his two children dead. He was long wanted in Israel for the attack considered one of the grisliest in Israeli history.
Kantar and four Hezbollah guerrillas were freed in 2008 in exchange for the bodies of two Israeli soldiers captured by Hezbollah in 2006, whose capture sparked a 34-day war between Israel and Hezbollah.
Kantar's release was highly controversial in Israel, where he is believed to be the perpetrator of one of the most notorious attacks in Israeli history.
He was sentenced to three life terms after he and three other Lebanese infiltrated Israel in 1979 and staged an attack in the northern coastal town of Nahariya.
An Israeli court convicted Kantar of killing a policeman and then kidnapping a man and his 4-year-old daughter and killing them outside their home.
As the attack unfolded, the girl's mother hid inside a crawl space inside their home and accidentally smothered their crying 2-year-old daughter, fearing Kantar would find them.
Two of his co-conspirators were killed in a shootout with police. The third was also convicted and sent back to Lebanon in the 1980s as part of a prisoner swap.
Kantar received a hero's welcome upon his return to Lebanon in 2008. Assad awarded him the country's highest medal during a trip he made to Damascus that year.
Kantar is the most high profile Hezbollah fighter to be killed since last year.