Asked about the missile attack, an Israeli military spokesman told Reuters, "We don't comment on such reports".
Mr Joudeh added shortly after that "another air defence missile was just launched".
The news agency did not give further details and it was unclear who was behind the attack, which Syrian state television branded as an "aggression".
It is now unclear what the airstrike was targeting.
The same air base was targeted by United States missiles in 2017, after it was suspected of being involved in a previous chemical attack that killed at least 70 people in the rebel-held town of Khan Sheikhoun.
They added that several explosions were heard near the base.
There are now no reports of targets hit in Damascus.
The Pentagon said there were no reports of USA military activity, after reports from Syrian television that Syrian air defences responded to a missile attack over Homs which targeted Shayrat air base late Monday night.
Israel has previously carried out air strikes during the conflict in Syria, targeting Iran-backed militias fighting alongside the forces of Syrian President Bashar al-Assad.
"There is no USA military activity in that area at this time", Eric Pahon, a Pentagon spokesman said.
The recent incident follows a coordinated attack by the US, UK and France that saw over 100 missiles launched from US ships and UK Tornado fighter-bombers.