The club’s £7m striker will be missing until after Christmas with ligament damage suffered in an Under-23s game between Leeds and Bristol City last week.
Bamford limped from the field during the first half of Friday’s 5-0 win at Elland Road and was sent for a series of scans and assessments over the weekend.
Further tests on Monday revealed an injury to his posterior cruciate ligament, a problem which could potentially have ended his season a month after his arrival from Middlesbrough.
Leeds spent heavily on Bamford six weeks ago, making him their most expensive arrival since Robbie Fowler in 2001, and the club expected the 25-year-old to make a big impact on their Championship term despite him starting the campaign on the bench.
He came onto the club’s radar towards the end of the transfer window after prior negotiations with Abel Hernandez and Matej Vydra fell through.
Bamford, who scored his only Leeds goal to date in a League Cup win over Bolton Wanderers, is yet to make a league start and was one of a number of senior players used in Friday’s development squad match. His absence leaves in-form Kemar Roofe as the only proven forward available to Bielsa.
Director of football Victor Orta said: “This is clearly disappointing news for Patrick and everyone connected with Leeds.
“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 an important role.”
Leeds have been affected by a spate of injuries during the early stages of the season, with Adam Forshaw forced to miss the opening six league games with a broken foot and Liam Cooper, Pablo Hernandez and Stuart Dallas consigned to the sidelines by more minor issues.
All four of those players are likely to be available for Saturday’s game at Millwall but defender Gaetano Berardi remains a doubt with a knee problem sustained in a 0-0 draw with Middlesbrough before the international break.
Leeds appointed former Hull City and Liverpool employee Rob Price as their new head of medicine and performance during the summer, bringing in a specialist with a reputation for ensuring the quick return of injured players.
Price said: “Patrick is a very fit footballer and whilst this is a setback, we’ve spoken to some of the best consultants in the country to make the correct diagnosis quickly.
“My team will work with Patrick to get him back involved with the first team as fast as possible.”