No one was injured, a police spokesman told AFP.
The protesters, Syrian nationals, broke through a gate in the fence and then penetrated the building, where they found the ambassador.
"The ambassador also resides there," the spokesman said. "He alerted the police and asked them to take measures on Syrian territory," he said, referring to the grounds of the embassy.
Police escorted the intruders from the building and took their personal details. About six of the demonstrators outside the building pelted it with paint bombs.
One person was briefly detained and released while another demonstrator was taken into custody on an outstanding arrest warrant.
Meanwhile in the northern German port city of Hamburg, about 30 people invaded the city's Syrian consulate building, breaking windows and the front door and daubing graffiti in Arabic on the walls, a police spokesman said.
Eight of the demonstrators had Danish passports, the spokesman said, adding that the nationality of the other protesters was not immediately clear. Police made four arrests and one person was treated for injuries in hospital.
The incidents came after a mass rally in Syria Saturday against the regime of Bashar al-Assad. About 50,000 people gathered for the funeral of Meshaal Tamo, a Kurdish opposition figure killed on Friday.
Syrian security forces killed at least two mourners and wounded several others when they fired on the crowd in the city of Qamishli, activists said.
In Vienna, 11 people were arrested for invading the Syrian embassy and protesting on its balcony overnight Saturday, Austrian police said.
British police said yesterday they had arrested seven protesters outside the Syrian embassy in London, including three men who climbed onto the roof of the building and waved the Kurdish flag.
And late Saturday five Syrian Kurdish protesters were detained for illegally entering the offices of Syria's permanent mission to the United Nations in Geneva.