The 24-year-old only joined Leeds this summer, making the move from Middlesbrough for a fee potentially rising to £10m.
He has largely played second fiddle early on in his Elland Road career, with Kemar Roofe starting the season in fine form for Marcelo Bielsa's side.
Bamford suffered the injury when playing for Leeds U23s in their game against Bristol City on Friday.
"This is clearly disappointing news for Patrick and for everyone at Leeds United, said director of football Victor Orta.
"Patrick has settled in well, quickly becoming an important player for Marcelo Bielsa and a popular part of the group.
"We have an excellent medical team at the club and Patrick is in the best possible hands, he will be back available to us during an important part of the season and he will still play a key role in our campaign."
Despite the set-back, the club's head of medicine and performance Rob Price was confident that Bamford would be back on the pitch as soon as possible.
"Patrick is a very fit footballer and whilst this is a setback for all concerned, we have spoken to some of the best consultants in the country to make the correct diagnosis quickly," he explained.
"My team will work with Patrick to get him back involved with the first team as fast as possible."