The UN office for the Coordination of Humanitarian affairs (OCHA) said at least 50,000 people had been displaced within Hasakeh while another 10,000 had fled north towards the town of Amuda.
A Syrian OCHA official told AFP that the displaced included ethnic Arabs and Kurds.
IS jihadists captured two southern neighbourhoods in Hasakeh, the capital of the province by the same name, yesterday, the Britain-based Syrian Observatory for Human Rights monitor said.
"Should the security situation continue to deteriorate, it is estimated that up to 200,000 people may try to flee Hasakeh city in the coming hours and days, most likely towards Amuda and Qamishli" to the northeast, OCHA said.
Hasakeh had a pre-war population of 300,000, including Muslim Arabs, Kurds, and Christians, according to OCHA estimates.
UN agencies and their partners in Qamishli were preparing for an influx of displaced people yesterday, OCHA said.