An eight-year-old girl was killed and 11 people were injured in the blasts in the upscale Abu Rummanah area of Damascus on Saturday, the SANA news agency said.
One shell fell near a school and the other on a roof, damaging several shops and cars.
The blasts struck some 300 meters (1,000 feet) away from the Four Seasons Hotel where the chemical inspectors and UN staff are staying. A UN employee staying there said it did not appear that the hotel was affected by the twin explosions. The hotel remained open after the blasts, he said, speaking on condition of anonymity because he was not authorized to speak to reporters.
He said the first explosion was heard at about 11:15 a.m., followed by a second. Thick smoke rose from the area and ambulance sirens sounded shortly afterward.
Foreign-backed militants routinely fire mortar shells from the outskirts of Damascus at city neighborhoods. Last week, a similar attack killed eight people in al-Qasaa Christian neighborhood.
Inspectors from the Organization for the Prohibition of Chemical Weapons and UN staff have been in Syria for the past two weeks to destroy the country's chemical weapons stockpile.
The OPCW inspectors have so far visited three sites linked to Syria's chemical weapons program, though the agency has not provided details. On Saturday, before the mortar attack, a convoy of UN cars left the Four Seasons, but its destination was not known.
The inspectors' mission in Syria is unprecedented because of a tight timetable - they are to get the job done by mid-2014 - and because they are operating in the midst of a civil war.
They are to inspect more than 20 sites, some close to front lines crisscrossing the country.
The Syrian conflict erupted in March 2011. More than 100,000 people have been killed since then and millions of Syrians have been displaced.
RA/HH