The Cowboys confirmed on Friday Morgan had a partial tear in his posterior cruciate ligament after hurting his knee in Queensland's 26-16 Origin victory against NSW in Brisbane on Wednesday.
Morgan is expected to be sidelined for up to a month, with the club expecting him to return for their NRL round 20 clash against Canterbury on July 21.
The Cowboys have the bye the weekend before, meaning there is still a chance Morgan could be fit for the final Origin game in Sydney on July 13.
With Morgan's usual replacement Ray Thompson also sidelined with a knee injury, Cowboys coach Paul Green has some decisions to make before Monday's NRL clash with Manly.
Fullback Lachlan Coote may move into the halves alongside captain Johnathan Thurston with youngster Jahrome Hughes to take the No.1 jersey.
North Queensland's NSW prop James Tamou picked up a minor neck complaint in Wednesday's Origin clash and will be monitored before a final decision on whether he'll play the Sea Eagles is made.