It was not clear if the diplomatic mission was specifically targeted in the early morning attack on Tuesday, which damaged the roof.
The building is located on the edge of the upscale Damascus' district of Abu Roummaneh.
No casualties were reported.
There was no claim of responsibility for the attack, the latest in the string of assaults on foreign diplomatic missions in Damascus.
Rebels fighting to topple President Bashar Assad have frequently fired mortars into Damascus to disrupt life in the capital, where the government tries to portray the situation as normal despite the civil war raging well into its third year.