The number is far short of the hundreds of thousands that aid agencies have been bracing for but the offensive is still in its early stages and many more are expected to flee as troops approach the city itself.
On Tuesday, there was "a big wave of displaced people that is considered the greatest number since the start of the military operation to liberate Nineveh province," Displacement and Migration Minister Jassem Mohammed al-Jaff said in a statement.
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"The ministry received and transported more than 3,300 displaced people" to camps, he said.
Most fled homes in Nineveh province, of which Mosul is the capital, but some left from Kirkuk to its west or Salaheddin to its south.
According to a UN tally, 8,940 people have been displaced since the operation to recapture Mosul from the Islamic State group began on October 17.
The number so far is a drop in the ocean compared with the more than three million people who have been displaced by violence in Iraq since the start of 2014.
But the UN refugee agency expects tens of thousands to flee in the coming days and is establishing camps with a total of 30,000 tents, enough to accommodate 150,000 people.