The 18-year-old, who has scored four goals this season, suffered the injury in training last month ahead of the Scottish Communities League Cup semi-final against Inverness and has no chance of making the final against St Mirren on March 17.
Hearts manager John McGlynn said: "Callum Paterson is having an operation on his foot today (Thursday). It looks like three months so that will take him to the end of the season.
"He is going to get a pin in his foot."
Paterson established himself as a regular after McGlynn handed him his debut in the opening game of the season against St Johnstone, and has gone on to make 27 first-team appearances.
The teenager made his debut at right-back before being moved into midfield and then up front, scoring his first two goals in a victory at Dundee United in September.
McGlynn, whose team return to Tannadice on Saturday, said: "It's a blow for the boy and a blow for the team as well.
"Callum came on the scene at 17 years of age, broke into the first team and got himself four goals. He has had a great season.
"Then after a freak training ground accident he will have to go through an operation.
"He will probably feel the whole world has caved in on him. It will take him right to the end of the season, but we will support him."