At least half of the dead were reported to be women and children.
The Sana news agency said a car packed with explosives blew up near a school in a residential part of Qatana suburb, south-west of the capital.
The report quoted medics from a nearby hospital as saying that 16 people were killed, including seven children and “a number” of women. Nearly two dozen other people were injured.
Anti-regime activists say more than 40,000 people have been killed since the start of the uprising against President Bashar Assad’s regime in March 2011.
The blast is the latest in a string of similar bombings in and around Damascus that the government says have killed at least 25 people in the last two days.
While no one has claimed responsibility for the bombings, some have targeted government buildings and killed officials, suggesting that rebels who can not engage Assad’s forces directly in Damascus are resorting to other means.
Similar attacks hit four places in and around Damascus on Wednesday. Three bombs collapsed walls of the interior ministry building, killing at least five people. One of the dead was Syrian parliament member Abdullah Qairouz, Sana reported.
Other explosions on Wednesday hit near the Palace of Justice, in the suburb of Jermana and in the upscale Mezzeh 86 district, heavily populated by members of Assad’s minority Alawite sect. One of the three killed in that that bombing was a state TV journalist named Anmar Mohammed, Sana said.
The Syrian Observatory for Human Rights said the number of those killed in the interior ministry bombing had risen to nine. The Observatory, which is based in Britain and relies on contacts inside Syria, also reported clashes between rebels and regime forces in a number of areas south of the city as well as government airstrikes on suburbs to the city’s east and south.