"General Mohammad Ali Allahdadi and a number of fighters and Islamic Resistance (Hezbollah) forces were attacked by the Zionist regime's helicopters," said a statement on the Guards' website.
"This brave general and some members of Hezbollah were martyred," it said, adding that Allahdadi was in Syria "as an adviser helping the Syrian government to confront takfiri Salafist (Sunni extremist) terrorists".
Shiite Iran is Syrian President Bashar al-Assad's main regional ally in his war against the mainly Sunni rebels seeking to overthrow him.
A source close to Hezbollah earlier told AFP that six Iranian soldiers, including commanders, died alongside six of its own fighters in the attack, but the Guards made no mention of other losses.
The raid, near Quneitra on the Syrian-controlled side of the Golan Heights on Sunday, enraged Hezbollah's supporters, but analysts said the group would seek to avoid a major escalation with Israel.
Hezbollah officials said Jihad Mughniyeh, son of the group's late commander Imad Mughniyeh, would be buried on Monday afternoon in Beirut's southern suburbs. Massive crowds were expected.
Once solely focused on fighting the Jewish state, Shiite Hezbollah is now deeply involved in the war in neighbouring Syria, where it backs Assad.
The six fighters killed on Sunday afternoon were carrying out a field reconnaissance mission in Mazraat Amal village, Hezbollah's Al-Manar television said.
An Israeli security source confirmed a helicopter had carried out a strike against "terrorists" in the Golan who were allegedly carrying out an attack.