The figure increased significantly over the past week as forces battled deep into the densely populated city, but it falls short of pre-offensive predictions.
"68,550 people are currently displaced and in need of humanitarian assistance," the United Nations' Office for the Coordination of Humanitarian Affairs said in a statement.
OCHA said the aid response to the offensive launched against the jihadists on October 17 was growing in complexity, with varying needs for different categories of civilians.
"Humanitarian needs are severe among displaced families in and out of camps, vulnerable residents of retaken communities, and people fleeing the intense fighting in Mosul city," it said.
A million-plus civilians were thought to still live inside Mosul, the country's second city and the jihadists' last major bastion in Iraq, before the operation was launched.
The number of people displaced since the start of the offensive "is less than we expected -- we should be able to handle this relatively small number easily", Iraqi Foreign Minister Ibrahim al-Jaafari told reporters after a meeting in Budapest.
The UN had initially predicted that 200,000 civilians could be forced from their homes in the first few weeks of the offensive, Iraq's biggest military operation in years.
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Still no safe routes
Iraqi forces have so far been sending the message to the population of Mosul that they should stay at home and not try to flee through the front lines.
Many residents of Mosul have indeed hunkered down in their houses as Iraqi forces took on IS fighters in fierce street battles.
That has however restricted both the government forces' ability to use heavier weaponry against the jihadists and aid groups' ability to deliver assistance to civilians in need.
"While Mosul is under ongoing heavy attack, there are currently no safe routes out of the city," Norwegian Refugee Council (NRC) spokeswoman Becky Bakr Abdulla told AFP.
"Civilians are facing an extremely difficult decision of either staying in their homes stuck in the crossfire or risk their lives in an attempt to find their way out of the city," she said.
The lower than expected displacement from the city of Mosul has allowed aid organisations to keep up with the number of displaced people in need of shelter.
According to the UN, the majority of the displaced are housed in camps, whose capacity is being increased daily and is slated to reach around half a million by mid-December.