The 25-year-old forward suffered the problem on Saturday during Boro's goalless draw at Bournemouth in the Championship.
He will now undergo surgery in an attempt to get him fit for the start of next season.
"Following scans and consultations in London, it has been confirmed that Muzzy Carayol has torn his anterior cruciate ligament," read an official club statement.
"He will be operated on by world-renowned English specialist Andy Williams in two weeks' time once the swelling has gone down."
Carayol had scored eight goals in 33 games for Boro before suffering the injury.