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.
"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."
While McGlynn has lost Paterson, he is set to gain right-back Jamie Hamill, who returned to full training this morning almost 10 months after rupturing a cruciate ligament.
The former Kilmarnock player's recovery suffered a setback around the turn of the year, but extra rehabilitation work has got him back with his team-mates and he will now look for under-20s action.
"It's good to get Jamie back," McGlynn said.
"I've not had the benefit of working with Jamie.
"We won't rush him back into the first team, there is no point rushing him after all this time.
"But knowing Jamie, he will be pushing for a cup final place."
Meanwhile, midfielder Jason Holt is expected to shake off an ankle injury, which forced him out of the Scotland Under-21 squad, to be fit for the Clydesdale Bank Premier League clash on Tayside.