Four people have been killed and others injured in the Hamah attack, reports the British-based Syrian Human Rights Observatory (SOHR). According to the organization, the airport has been knocked out.
The Israeli military confirms the attacks in a statement and says they target military bases and other "military infrastructure".
The facility in Damascus, located in the Barzeh district, has been attacked before.
Since the Islamist HTS movement overthrew Bashar al-Assad's regime in December, Israel has carried out several hundred attacks on targets on Syrian soil. Prime Minister Benjamin Netanyahu said in February that southern Syria must be completely demilitarized.