Police have cordoned off the area. Officials say six Yemeni soldiers were among the dead.
Witnesses also say they heard gunfire near the embassy after the explosions.
In recent years, Islamic extremists have carried out several attacks in Yemen targeting Americans.
Last April, the U.S. State Department ordered non-essential staff to leave Yemen, following a militant attack on a residential compound and an al-Qaida attack targeting the U.S. embassy.
Yemen is the ancestral homeland of al-Qaida leader Osama bin Laden.
Some information for this report was provided by AP and Reuters.
By VOA
From Wikipedia
Sana lies in the heart of Yemeni highlands on a plateau at an altitude of 2,200 m (7,220 ft) surrounded by several mountains, notably Jabal Nuqum and Aiban. It has a cool and dry climate and in the winter time light frost is possible. Extreme recorded temperatures are −3 °C (27 °F) and 34.4 °C (93.9 °F). The city enjoys a fair weather during the months of April to October. Afternoon thunderstorms are common which brings much of San'a's annual rainfall. The city is around 370 km (230 mi) north of Aden, the economical and financial centre of Yemen.
