The warning came via text message, urging the sick and wounded to flee before a "strategically planned assault using high precision weapons occurs within 24 hours."
Rebels were also given an ultimatum to lay down their arms and renounce their leadership, or be killed.
The message was likely sent by the Syrian government as the regime is likely the only party capable of sending a mass text to the entire population.
While there were no reports of a bombardment by Monday afternoon, witnesses told CNN that fighter jets had been spotted in the city, as deadly skirmishes were reported all over Aleppo.
Russian warplanes have since September last year backed the regime with airstrikes over rebel-held positions, pounding eastern Aleppo, where schools and hospitals have been crushed.
The text message warning is seen as a response to Syrian rebels launching an offensive
last month to break the regime's siege on eastern Aleppo.
Assad: Go back to Turkey, or die
Russia is the most powerful sponsor of Syrian President Bashar al-Assad's regime, and its air power has been a key factor in helping the government solidify its control over the city.
Assad has insisted that he has no option but to "to clean" Aleppo and press on with the offensive.
"You have to keep cleaning this area and to push the terrorists to Turkey ... to go back to where they come from, or to kill them," he said.
"It's going to be the springboard, as a big city, to move to other areas, to liberate other areas from the terrorists. This is the importance of Aleppo now."
Fresh clashes broke out Sunday, with regime shelling killing at least 11 people in the al-Salehin neighborhood, according to the Aleppo Media Center activist group. Several other neighborhoods were shelled by ground artillery and heavy machine gunfire from helicopters, the UK-based Syrian Observatory for Human Rights (SOHR) said.
Rebel factions targeted army positions on the northern front line, causing casualties among Syrian troops, the SOHR said.
The Syrian Army accuses rebels in eastern Aleppo -- who they call terrorists -- of using civilians as human shields.
The UN warned last week that eastern Aleppo was on the brink of starvation ahead of a "killer" winter.
Residents there told CNN that their food stocks were running out, and that markets that once sold fruit and vegetables were now empty. A kilogram of meat, they said, costs around $40, a price that most in Aleppo simply cannot pay.
The last significant aid delivery was in July, and the area is extremely low on medicine and much-needed fuel to run hospital generators and ambulances.
The city has seen considerable death and destruction wrought by the civil war that has raged for more than five years.
About 1.5 million people still live in the regime-held parts of Aleppo, while 250,000-275,000 residents are in the devastated rebel-held east, according to the UN.
In July, about 200,000 people fled the city over a two days, according to a UN official,
citing the International Committee of the Red Cross and the Syrian Arab Red Crescent
Turkey eyes Kurdish-held city
Turkey has been carrying out airstrikes
in northern Syria to back the Free Syrian Army (FSA), which is currently moving in on the ISIS-held city of al-Bab. The city lies strategically between Aleppo and the ISIS heartland of Raqqa.
The Turkish Army said it hit 15 targets on Sunday, including two ISIS "headquarter" buildings, an ammunition storage and 10 defense fronts.
Ankara has said once the city is liberated, it plans to move on to Manbij, stirring sectarian tensions that complicates internationally backed operations to free Syrian cities from ISIS control.
Manbij was in August freed from ISIS rule by the Syrian Democratic Forces
(SDF), an alliance of Kurdish and Arab groups. But Turkish President Recep Tayyip Erdogan last month said Ankara would not allow the Kurds to hold any territory west of the Iraqi city of Mosul. Manbij is just 40 kilometers south of the Turkish border.
Turkey considers some of the Kurdish militia groups in the alliance as terrorists, including the YPG. But the SDF is supported and armed by the US, further complicating the conflict, which has already put Washington at loggerheads with Moscow.
The former Cold War enemies, both of which are carrying out airstrikes in Syria, have long feuded over which groups should be targeted. The US supports and arms groups that it considers "moderate rebels," while Russia calls any rebel group that is opposed to the regime "terrorists."