A video posted on the internet showed rebels in camouflage and black scarves driving a tank into the al-Omar field in Deir al-Zor province.
“We are now inside the al-Omar field, the biggest field in Syria. Seven tanks, two BMPs (amphibious armoured vehicles) and all the weapons and vehicles inside the field were captured,” the speaker said.
The speaker added that the field was overrun early on Saturday, but the footage could not be independently verified.
There was no immediate comment from the government of president Bashar al-Assad.
A pipeline transporting crude oil from al-Omar to central Syria for refinement had still been working despite the civil war, which began in 2011.
Opponents of the government said the loss would be a major blow for Assad.
Rami Abdelrahman, head of the pro-opposition Syrian Observatory for Human Rights, said: “Now, nearly all of Syria’s usable oil reserves are in the hands of the Nusra Front and other Islamist units. The regime’s neck is now in Nusra’s hands.”
Losing the al-Omar field would mean Assad’s forces would be almost completely reliant on imported oil in a highly mechanised military campaign to put down the uprising.
But it is not yet clear how much the loss of the field would affect government forces on the battlefield.
Assad is believed to be getting fuel from Shia Iran, Syria’s main regional ally.
Syria is not a major oil producer and has not exported any oil since late 2011, when international sanctions took effect to raise pressure on Assad.
Assad’s forces have gained momentum against the rebels in recent months but opposition fighters, particularly powerful Islamist factions, still hold large swathes of territory in northern and eastern Syria.
Rebels, pro-government forces and local tribes have been fighting each other and sometimes even among themselves to seize oil reserves in the east of the country.