They would join more than three million Iraqis who have already been driven from their homes by violence over the past two-and-a-half years.
"The International Committee of the Red Cross believes that up to a million more people could be forced to flee their homes in Iraq in the coming weeks and months," the Red Cross said in a statement.
"More than 10 million people are already in need of assistance in the country. More than three million people are already internally displaced," it said.
"If there is the predicted upsurge in violence, then the figure of internally displaced could dramatically increase."
Signup to our newsletter and follow us on Facebook and Twitter!
Iraqi forces are conducting operations aimed at setting the stage for an assault on Mosul, a northern city that has been held by IS since June 2014.
Mosul was once home to some two million people, but the current population has been estimated at around half that figure.
The operation to retake the far smaller city of Fallujah, located much closer to Baghdad, pushed tens of thousands of people to flee, catching the aid community flat-footed and leaving many people in appalling conditions.
The scale of displacement as Iraqi forces fight to retake Mosul will be much larger, and people may flee to areas that could be much more difficult for relief agencies to reach.
The Red Cross said it is asking for an additional $17.1 million (15.6 million euros) for its Iraq budget to help provide assistance to displaced people in the country.
IS overran large areas north and west of Baghdad in 2014, but has since lost significant ground to Iraqi forces backed by US-led air strikes.