The ministry said Israel fired “bursts of missiles” from northeast of Israel’s Lake Tiberias, targeting the airport and several security checkpoints south of the capital.
Syrian air defenses shot down some of the missiles, he added.
There was no immediate confirmation whether the strike affected airport operations.
The Israel Defense Forces said it would not comment on foreign media reports.
An Israeli missile strike in the countryside around Damascus killed three Syrian soldiers last month. Airstrikes in June put Damascus airport out of service for almost two weeks.