The 21-year-old forward sustained the injury when he was hit by Los Angeles Kings defenseman Matt Roy in the first period of the Maple Leafs' 5-0 win on Dec. 8.
Robertson was initially expected to miss 6-8 weeks after choosing to attempt to rehab the injury, but it was decided recently that surgery would be required. The expected recovery time is six months.
"The process was as we talked about when he first had his injury," Maple Leafs coach Sheldon Keefe said Tuesday. "It was one of those where we wanted to give some time to rehab and see how it was going to go and reassess from there but over time it was determined surgery was the best option for him."
Robertson, who was selected by Toronto in the second round (No. 53) of the 2019 NHL Draft, has five points (two goals, three assists) in 15 games this season and seven points (three goals, four assists) in 31 NHL games.
He scored two goals, including in overtime in a 3-2 win against the Dallas Stars in his season debut on Oct. 20. They were his only two goals this season.
It is the third significant injury Robertson has sustained in as many seasons.
In his season debut for the Maple Leafs in 2020-21, he sustained a knee injury that caused him to be out for four weeks. Early last season while playing for Toronto of the American Hockey League, Robertson sustained a non-displaced fracture in his right fibula that caused him to be sidelined 10 weeks.
"In terms of what I said to him was just encouraging him that despite the adversity he's had with his injuries, he has found ways each time to bounce back and still show progression in his game and it hasn't seemed to stall him in his development," Keefe said.
"We saw what type of training camp he had this year, he came in and gave us some good minutes at the NHL level. So he's been in this situation before. You can never question his work ethic and commitment and all of that so he's going to put in all of the work to do all that he can to bounce right back again."