The overnight barrage from nearby hills followed the withdrawal of hundreds of troops backed by tanks that had entered the city on Wednesday to root out rebels, the sources said. About 200 people were wounded in the shelling, they said.
A main oil pipeline from Deir al-Zor province feeds Syria's two refineries, in the city of Homs and an export terminal on the Mediterranean. Large swathes of the province have fallen into rebel hands in the past few months.
"Deir al-Zor was hit by a few artillery rounds during the first army attack on the city back in August, but this is the first time we have seen sustained shelling," said a source at a hospital in the city, who spoke on condition of anonymity.
"Two rebels were among those killed. The rest of the casualties were mostly civilians."
Syria has restricted media access since the start of the uprising against President Bashar al-Assad in March 2011, making it hard to verify accounts from authorities or activists.
The shelling damaged dozens of houses on Port Saeed street and in the al-Jubeila neighbourhood, where a Ministry of Finance department building was hit, opposition campaigners said.
Two rounds fell on the site of regular rallies against Assad in the al-Hamidiyeh neighbourhood, but no protesters were there, the sources said.
Insurgents fought back against the ground offensive on Wednesday with rocket-propelled grenades, hitting four armoured vehicles. Saleh al-Shohat, a rebel commander, was killed by tank fire, they said.
In the past week Free Syrian Army fighters have attacked roadblocks and tanks on the road from Deir al-Zor to the Iraqi border, killing or wounding dozens of troops and destroying several tanks and armoured personnel carriers, opposition sources said.
The government has lost control of parts of the province as alliances between Assad's ruling elite - from the Alawite minority - and Sunni tribes have collapsed, leaving the army with stretched supply lines, opposition sources and diplomats said.