Her mother went into labour soon after the disaster and gave birth before she died, a relative said. Her father, four siblings and an aunt were also killed.
Dramatic footage showed a man carrying the baby, covered in dust, after she was pulled from debris in Jindayris.
A doctor at a hospital in nearby Afrin said she was now in a stable condition.
The building in which her family lived was one of about 50 reportedly destroyed by a 7.8-magnitude earthquake in Jindayris, an opposition-held town in Idlib province that is close to the Turkish border.
The baby's uncle, Khalil al-Suwadi, said relatives had rushed to the scene when they learned of the collapse.
"We heard a voice while we were digging," he told AFP news agency on Tuesday. "We cleared the dust and found the baby with the umbilical cord [intact], so we cut it and my cousin took her to hospital."
Paediatrician Hani Maarouf said the baby had arrived at his hospital in a bad condition, with "several bruises and lacerations over all her body".
"She also arrived with hypothermia because of the harsh cold. We had to warm her up and administer calcium," he added.
She was photographed lying in an incubator and connected to a drip, as a joint funeral was held for her mother Afraa, father Abdullah and her four siblings.
They are among 1,800 people known to have been killed by the earthquake in Syria, according to the Damascus-based government and the White Helmets, whose volunteer first responders operate in opposition-held areas.
Another 4,500 people have been killed in Turkey, where the epicentre was.
The White Helmets have so far reported 1,020 deaths, but they have warned that figure is expected to "rise dramatically".
"Time is running out. Hundreds still trapped under the rubble. Every second could mean saving a life," they tweeted on Tuesday.
"We appeal to all humanitarian organisations and international bodies to provide material support and assistance to organisations responding to this disaster."
The UN has vowed to use "any and all means" possible to get aid to people in the north-west, but it has said that deliveries have been halted temporarily due to damaged roads and other logistical issues.
It has also urged governments not to politicise aid delivery when so many are in desperate need.
A UN Security Council agreement authorises the use of just one border crossing for deliveries from Turkey into the north-west. All other deliveries are meant to go via Damascus, although in the past the government has facilitated only a small amount of "cross-line" aid.
Even before the earthquake struck, 4.1 million people in the north-west - most of them women and children - were relying on humanitarian aid to survive.