A US-backed alliance of Kurds and Arabs has also surrounded the IS stronghold of Manbij about 100 kilometres (60 miles) northeast of Aleppo city.
Air strikes by the US-led coalition killed at least 21 civilians in and around the jihadist bastion on Monday, said the Syrian Observatory for Human Rights.
In Aleppo city itself, air strikes struck rebel areas, killing four civilians in Qaterji, the monitor said.
In Bab al-Hadid, another district that was hit, an AFP correspondent saw a man searching for his family under the rubble.
He called out to his daughter, who replied: "I'm in the basement. There's no air," before she fell silent, and he burst into tears.
Bombs then dropped nearby causing more casualties, including a woman who lost a leg, said the correspondent, who noted attacks on eastern Aleppo had intensified in recent days.
Food and fuel shortages had already hit rebel-held districts that are home to at least 200,000 people, after government forces advanced to within firing range of the key Castello Road supply route on July 7.
- 'Nowhere to go' -
Regime forces seized the road itself at the weekend, completely severing the rebel-held portion of the city from the outside world and raising fears of a potentially devastating siege.
"I don't know what is going to happen to us," said 38-year-old Mohamed Rukby, an unemployed father-of-four in the Bustan al-Qasr neighbourhood.
"We have nowhere to go. All the roads are closed and we've been suffering for days with shortages of bread, food and basically everything."
In the opposition-controlled Al-Mashhad district, mechanic Mohamed Zeitun said his work had dried up because fuel shortages meant residents were not driving anywhere.
"The idea of the siege keeps me up at night," the 44-year-old told AFP.
"I don't have supplies to last me more than a week, and if there is no food in the markets, there could be a famine," said the father-of-five.
Aleppo city was once Syria's economic powerhouse, but it has been ravaged by the war that began in March 2011 with anti-government protests.
The conflict has killed more than 280,000 people and left Aleppo divided roughly between government control in the west and rebel control in the east.
Analysts said the government advance was a significant blow to the rebels.
"It has now become mission impossible for Syria's rebels who are completely deprived of any breathing space," said Karim Bitar, an analyst at the Paris-based Institute of International and Strategic Relations.
The advance also leaves Syria's President Bashar al-Assad feeling "considerably more secure than a few months ago," he said, meaning his forces could move "to further consolidate his positions".
- 'Devastating blow' -
The encircling of eastern Aleppo has raised international concern, with the UN's humanitarian coordination body OCHA warning that "the situation is particularly worrying due to the high concentration of people living in this area".
It said eastern Aleppo had not received humanitarian supplies since July 7, and that there was enough food there to last 145,000 people for one month.
OCHA said some essentials had been stockpiled and there were sufficient emergency medical supplies for four to five months.
But "further life-saving aid is needed urgently", it added.
In some places, civilians have reportedly starved to death or died for lack of medical supplies because of siege tactics.
Despite successive rounds of talks, international efforts to find a solution to the conflict have yet to bear fruit, and UN Syria envoy Staffan de Mistura has urged Russia and the United States to push for renewed peace talks in Geneva next month.
But the opposition High Negotiations Committee said the regime's advance around Aleppo could jeopardise new talks.
"This is pushing the negotiations in Geneva to a more remote date. Frankly the prospects are becoming less and less possible or more and more remote," HNC member Basma Kodmani said late Sunday.
Syria expert Aron Lund, at the Carnegie Endowment for International Peace, said that if Assad manages to secure both Damascus and Aleppo it would be a "devastating blow for his opponents".
"It wouldn't mean the war is over. The government is still weak and exhausted... But it might have severe repercussions for rebel morale and perhaps also for foreign support to the opposition," he added.