Sixteen were non-Syrian fighters, the group's head Rami Abdel Rahman said.
Iran has fought alongside Syrian President Bashar al-Assad's forces in the country's eight-year civil war, heightening Israeli concern over the presence of its arch foe along its border.
"Whoever hurts us, we will hurt him," Israeli Prime Minister Benjamin Netanyahu said in a statement.
"This is what we did overnight vis-a-vis military targets of the Iranian Quds Force and Syrian military targets in Syria after a barrage of rockets was launched at Israel."
The Israeli army said they had targeted about a dozen military sites, including warehouses and military command centres.
"It was very intense," spokesman Jonathan Conricus told AFP.
The most important target, he said, was a control facility at the main international airport in Damascus.
"It is the main building that serves the (Iranian) Revolutionary Guards... for coordinating the logistic facilities of transport of military hardware from Iran to Syria and from Syria onwards," he said.
Israel has carried out frequent air and missile strikes against Iranian targets inside Syria since the country descended into civil war in 2011, but rarely comments on them.
On Tuesday, four rockets were fired at Israel from Syria, with the army blaming an "Iranian force".
Israel's Iron Dome missile defence system intercepted the rockets.
Conricus said it was the sixth time Iranian forces had tried to attack Israel directly in recent years, most recently in August.
The Israeli attack Wednesday began in the early hours, with a series of large explosions rocking Damascus, an AFP correspondent in the city said.
Syria's state news agency SANA said Syrian anti-aircraft defences responded to a "heavy attack" by Israeli warplanes over the capital.