The shooting took place Saturday at the funerals of three youths killed a day earlier in an anti-Assad protest that was one of the biggest in the capital since a nationwide uprising started.
"They started firing at the crowd right after the burial," said a witness, speaking to Reuters in Amman by telephone.
People tried to flee and seek shelter in alleyways, he said.
The opposition Syrian Revolution Coordination Union said the gunfire near the cemetery had killed one mourner and wounded four, including a woman who was hit in the head. A shopkeeper told Reuters many protesters were arrested.
The Local Coordination Committees, an opposition activit group, said security forces had killed 14 people in Damascus and other parts of the country Saturday, including five in the opposition stronghold of Homs. None of the figures could be verified independently.