Police used teargas to keep the demonstrators away from the building.
The attack comes the day after the buildings housing the Danish and Norwegian embassies in the Syrian capital Damascus were set on fire. The Swedish and Chilean embassies, in the same building as the Danish mission, were also damaged.
No injuries have been reported in connection with the attacks.
The protests follow the publication of a satirical cartoons of the prophet Mohammed in Danish and Norwegian newspapers. The attack in Damascus followed SMS text messages which falsely claimed that people in the Danish capital Copenhagen planned to burn copies of the Moslem holy book the Koran.
Sweden’s Foreign Minister Laila Freivalds has strongly critcised Syria for allowing demonstrators to attack embassies. She tells Swedish Radio News that Syria’s Foreign Minister Faruq al-Shara has apologized, saying that no one could have known that the demonstrations would lead to violence.
The Swedish Foreign Ministry has recommended that Swedes avoid travel to Lebanon and Syria.