The incident comes after a unilateral three-day ceasefire declared by Russia and government forces ended on Sunday without any evacuations by the United Nations.
"Forty-eight people from... the eastern districts were able to flee towards the western districts, where a Syrian Arab army unit welcomed and secured them," SANA said late on Monday.
It accused rebel groups in the east of using civilians there as "human shields".
An AFP photographer saw three buses full of civilians on the government side of the Bustan al-Qasr crossing.
There was no UN presence, but a heavy deployment of government security forces.
Signup to our newsletter and follow us on Facebook and Twitter!
They were given government-provided aid and taken to temporary housing.
It was unclear whether they were civilians or rebels, which eastern districts they had left or how they had reached the western part of the city.
The brief ceasefire in Aleppo had been intended to allow civilians and rebels to leave the east via eight evacuation corridors.
But by the time it expired on Sunday, only a handful of civilians were reported to have used a single crossing point.
Nearly 500 people have been killed and more than 2,000 wounded since the Syrian army launched an operation to recapture eastern Aleppo on September 22.
The UN had asked Moscow to consider extending the pause until Monday evening, but there was no indication from Russia that it would do so.
More than 300,000 people have been killed in Syria and more than half of the country's population displaced since the conflict began in March 2011 with anti-government protests.