Pablo Marco, the regional manager of the charity known by its French acronym MSF, said concerns were rising for a large civilian population less than five kilometres (three miles) from advancing IS jihadists.
"We are talking about 100,000 people who are trapped a few kilometres from IS. They are terrified, there is nowhere to go," Marco said in a telephone interview with AFP.
IS swept towards the last rebel strongholds of Marea and Azaz in Aleppo province on Friday, forcing thousands to flee towards the northern frontier.
But Turkey has kept the border closed, leaving civilians stuck between the violent front line with IS to the east, the sealed border to the north, and the autonomous Kurdish canton of Afrin to the west.
"These people are now in a very small area of four by seven kilometres," said Marco.
"The situation is absolutely unsustainable and unacceptable for this population."
The United Nations has said the fighting has trapped up to 165,000 civilians between Azaz and the closed Turkish border.
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MSF's Marco said many of those who were fleeing the IS onslaught in recent days had already been displaced two or three times from other parts of the province.
"You can imagine how hard it is for them."
More than half of Syria's population have fled their homes since the conflict first erupted in 2011, with nearly five million escaping to neighbouring countries.
An estimated 6,000 people have escaped the fighting in Marea either towards the border or west towards the Kurdish-controlled region of Afrin.
But with limited resources, Marco said, Kurdish authorities would not be able to take in an influx of displaced individuals.
As the circumstances grow increasingly dire, Marco called on the Turkish authorities to allow safe haven for those fleeing IS's speedy advance.
"We know that the Turkish authorities are very concerned about the situation. They have made big efforts as you know, but the situation is so terrible that it justifies (opening the border)."
But he also called on the European Union "to do their part" to both support Turkey and take in more Syrian refugees escaping violence at home.
"All actors who are involved need to find a solution... This is really a shame."