Two rockets targeted the home of a senior figure of the Palestinian Islamic Jihad group at dawn, Akram al-Ajouri, "killing his son Muadh and another person", SANA said.
A civilian, Abdullah Yousef Hassan, was also killed in the attack, SANA reported.
Ten people were also injured in the strike, which partially destroyed a three-storey building in an area close to the Lebanese embassy.
The Islamic Jihad group confirmed al-Ajouri's son had been killed in the attack, which comes as a commander from the group was also killed in Israeli strikes on Gaza.
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"The home of a member of the political bureau of the Islamic Jihad movement in Palestine, Akram al-Ajouri, was also targeted in Damascus, killing one of his sons," it said.
The Israeli army did not immediately respond to a request for comment from AFP.
Israel has carried out hundreds of strikes on Iranian-linked targets in Syria, since war broke out in 2011.
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Israel targets Damascus home of Islamic Jihad official
Israeli airstrike on Damascus kills son of senior Islamic Jihad official
MENA
1 min read
Israeli airstrikes in Damascus have hit the home of an Islamic Jihad commander, killing his son.
The house of an Islamic Jihad figure was targeted in strikes [Getty]
An Israeli strike on Damascus on Tuesday targeted the home of a Palestinian Islamic Jihad figure, Syrian state news reported, as further strikes targeted the militant group in Gaza.
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