"A large number of food products are no longer available, and others have become increasingly difficult to find, driving up prices," the Syrian Observatory for Human Rights said.
The group said rebel forces have surrounded certain neighborhoods and the regime has been unable to deliver food, because a highway into the northern city from the south has been blocked and the airport closed.
Rebels moved into Aleppo exactly a year ago, and have since seized large swathes of both the city and the surrounding province.
But after months of fighting, a relative stalemate has set in, with the army unable to recapture much territory and rebels unable to take the city as a whole.
For now, the army is focusing its efforts in the central city of Homs, where it is trying to retake several rebel-held districts.
The fighting has created enormous destruction, and the Observatory said troops had brought in bulldozers on Tuesday to remove rubble as they advance.
The Observatory warned that civilians in the city were dying for want of medical equipment.
"The army's continuous bombardment over the past 11 days has made the critical humanitarian situation in rebel areas of Homs even worse," Observatory director Rami Abdel Rahman told Agence La Belle France Presse.
"An unknown number of rebels and civilians maimed in recent days are dying from their injuries, because there is no medical equipment to treat them," he added.
The Khaldiyeh and Old City neighborhoods of Homs have been under army siege for more than a year and since late June have come under steady shell and rocket fire as well as air strikes in a withering offensive by the regime.
"The little medical equipment the rebels could get into these areas was coming through underground tunnels. Now, these have been bombed too," Abdel Rahman said.
Activists on the ground confirmed the shortage of medical care.
"The medical community in the besieged areas of Homs is suffering from shortages," said Homs-based activist Yazan.
Large quantities of medical supplies had been used up due to the increased number of injuries caused by the shelling, Yazan told AFP via the Internet.
"This campaign on Homs has been the fiercest" since the start of the siege on rebel areas more than a year ago, he added.
Witnesses and activists have said Syria's forces have been joined in the assault by fighters from Lebanese Shiite movement Hezbollah.
At the start of the revolt against
Hereditary President-for-Life Bashir Pencilneckal-Assad
Leveler of Latakia...
in March 2011, Homs was dubbed "the capital of the revolution" when it was shaken by widespread protests against his rule.
Now, the rebels are caught in a small segment of the city, covering barely two square kilometers (less than a square mile) in the center.