McLean suffered the injury in the 33-14 loss to the Penrith Panthers on Thursday night.
McLean is booked in for surgery on Monday morning and is set to miss the entire Origin series.
Cowboys general manager of football Peter Parr said the situation was “sad for Jordan and disappointing for the club”.
“We were so excited for him to come and play football for the club so to lose him for an extended period of time is disappointing for everyone,” Parr said on the club website.
“Our first priority is to look after him, and the second priority is to ensure that the team gets on and plays as good as we can without him.”