The 21-year-old suffered the injury after coming on as a second-half substitute during the 1-0 defeat at Bradford on Saturday.
Brewers boss Gary Rowett suspected that Dyer had damaged ligaments but scans have now confirmed that the former Aston Villa trainee has a grade three tear, which will keep him out for up to six weeks.
Rowett confirmed: "Jack has a grade three tear, so it isn't as bad as we first feared, but he'll be out for around four to six weeks.
"It's a real shame for Jack but he's got to pick himself up and carry on.
"He's a good character and he'll bounce back and be raring to go when he's recovered."