The two bombs exploded as the bus, belonging to Syria's military, passed Damascus’ President’s Bridge, SANA reported, adding that experts defused a third bomb at the site.
No group has immediately claimed responsibility.
Also on Wednesday morning, 13 people were killed and more than 20 injured by Syrian regime shelling in northern rebel-held Idlib, according to the Syrian Observatory for Human Rights.
More than 350,000 people have been killed, according to United Nations figures, and millions displaced in a decade of civil conflict that began with the regime’s repression of anti-government protests. President Bashar al-Assad is now in control of about 70 percent of Syrian territory.
After the breakout of the conflict in 2011, several deadly attacks rocked the capital, but it has generally been spared violence in the past few years.
The province of Idlib is under the control of rebel groups, some with ties to jihadists. Turkish-backed militias control areas of the north, and a Kurdish-led administration governs the northeast.
Islamic State (ISIS) militants also remain a threat. The group was declared territorially defeated in Syria in 2019, but elements remain active, mainly in the north and east. ISIS in July 2019 claimed responsibility for a car bomb attack in Damascus.
In the latest edition of its weekly propaganda newspaper al-Naba released Thursday, ISIS claimed it had conducted one attack across Syria last week, killing and injuring three people.
Updated at 12:26pm
