The attack comes a day after Osama bin Laden's number two Ayman al-Zawahiri released a video warning of more attacks on US interests in the region.
There were conflicting reports of casualties, with one report saying a Syrian guard was shot dead.
Security agencies, fire engines and ambulances have been rushed to the area, which was cordoned off. The neighborhood also houses several other diplomatic missions and staff residences.
One witness was quoted as saying that two gunmen got out a car at the embassy entrance and shot at the guard before
A senior Chinese diplomat was among those injured in terrorist attack.
Li Hongyu, political counsellor at the Chinese embassy in Damascus, is in stable condition in a hospital, Foreign Ministry spokesman Qin Gang said in a statement posted on the ministry's website.
The official Xinhua news agency reported from Damascus that Li Hongyu, who was at the US embassy at the time of the attack, was hit in the face by flying shrapnel. The Chinese embassy is located close to the US embassy, both of which lie in the Abu Remmeneh district of Damascus.