Four blasts hit al-Tin Street near the al-Sadr hospital, with two explosions being car bombs and the others suicide bombers, the al-Ikhbariya channel said.
There are casualties among civilians in Sayeda Zeinab district, a police source, who talked to RIA-Novosti, said.
The death toll is currently being verified. Hezbollah's al-Mmanar TV puts the death toll at 22, while the Syrian state TV at 30. Dozens are feared injured.
#BREAKING: #Syria: Multiple explosions hit #Damascus district of Sayeda Zeinab - Reps Dead / Injed @Sindhleak pic.twitter.com/k5hOKfmJjeโ URGENT NEWS (@UrgentNews911) February 21, 2016
Earlier on Sunday, dozens of people were killed and injured in a double bombing attack in Homs. The local governor said that 34 people have died in the explosions, but RIA-Novosti cited a medical source, who said that at least 46 lives were lost, while 110 others were injured.
The Syrian Foreign Ministry said the bombing was aimed at derailing the ongoing peace talks between Damascus and rebel forces, and called on the UN Security Council to condemn the attack.
Bombings targeting civilians happen regularly in Syria, which has been riven by a five-year armed conflict.
Islamic State claimed responsibility for a bombing in Homs last month, which killed at least 24 people. Another attack in December claimed 32 lives.
Comment: The Syrian rebels can't win on the battlefield so now they take their suicidal missions into the cities, killing civilians.