In and around the border town of Azaz, families are sleeping in the streets, or up to 20 people to a tent, having left their homes with nothing but the clothes they were wearing.
The United Nations says up to 31,000 people have fled Aleppo city and surrounding areas in recent days, as government forces press an offensive that could encircle the rebel-held part of the city.
"There are no longer enough places for families to sleep," said Ahmad al-Mohammad, a field worker with Doctors Without Borders (MSF) who enters Aleppo province from Turkey daily.
"Many of them in the first days were sleeping in the streets and outdoors without blankets or covers," he told AFP.
He said up to 20 people were crowding into tents being distributed by aid groups and which are usually meant for seven only, with homes in towns receiving displaced people also filled to capacity.
"Most of the families left with just the clothes they were in," he said, adding that the cold and the crowded conditions were causing health problems including diarrhoea.
He said aid groups were also distributing warm clothes and mattresses, with Turkey allowing humanitarian goods across the border, which remains closed to the fleeing Syrians.
"They are trapped," Mohammad said in a late Monday telephone interview.
"They've left their homes and everything they have behind, and they can't get into Turkey."
The UN's humanitarian aid agency OCHA said on Monday that eight informal camps on the Syrian side of the border were at "full capacity."
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- Food urgently needed -
And the UN's aid chief Stephen O'Brien said he was "gravely concerned" by the mass displacement, noting that about 80 percent of the tens of thousands of people on the move were believed to be women and children.
"We have reports that civilians have been killed and injured, and that civilian infrastructure, including at least two hospitals, has been hit," he said in a statement.
"People urgently require shelter, food and basic household items."
He called on all parties to end targeting civilian infrastructure and allow civilians to move to safer areas.
Syrian government forces backed by allied militias and Russian air strikes began a major operation in northern Aleppo province last week.
They have advanced around much of Aleppo city, virtually encircling the rebel-held eastern part, and prompting tens of thousands to flee their homes in the northern countryside.
They are now around 20 kilometres (12 miles) from the Turkish border.
"It's the first time since 2013 that the Syrian regime has been this close to the Turkish border in Aleppo province," said Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights.
Turkey has said it fears the violence could drive up to 600,000 people to its border, in a "worst-case scenario."
While Ankara says its open-door policy to Syrian refugees remains unchanged, it has kept the main Aleppo border crossing closed in recent days, focusing on sending assistance to camps just inside Syrian territory.