The IOM "identified a total of 43,470 internally displaced Iraqis (7,245 families) from Fallujah district between 22 May and 13 June," it said in a statement.
It said 10,000 people had fled between June 11 and 13 alone.
The majority of the displaced were not from the city itself but lived in outlying areas.
Tens of thousands of civilians are still believed to be trapped in the centre, some of them being used as human shields by the Islamic State group.
Signup to our newsletter and follow us on Facebook and Twitter!
"Ongoing and recent displacement, especially from Fallujah, requires immediate attention," IOM Iraq chief of mission Thomas Lothar Weiss was quoted as saying in the statement.
"IOM is responding but funds and supplies are insufficient to provide adequate assistance to the huge numbers of displaced Iraqis," he said.
Fallujah is one of IS's most emblematic bastions and lies just 50 kilometres (30 miles) west of Baghdad, in the province of Anbar.
The latest wave of displacement brings to 3.3 million the number of Iraqis made homeless by conflict across the country since the beginning of 2014.
More than 40 percent of them are from Anbar, a vast Sunni province that borders Jordan, Syria and Saudi Arabia and was at the heart of the "caliphate" IS proclaimed two years ago.