The 21-year-old sustained a hamstring injury during the first half of the Blades’ 2-0 win against Peterborough and was forced off.
Heckingbottom revealed the former Liverpool forward would be going under the knife on Tuesday.
Quotes from the Blades boss on the club’s Twitter feed said: “He’s having an operation tomorrow, which will rule him out probably for the season.
“If he’s back before then it’s a bonus, but we’re not counting on it. We’re going to help him through it.”
Brewster joined Sheffield United in October 2020 and has made 16 appearances for the club this season.