King, who leads the FBS with 50 touchdowns responsible for this season, suffered the injury in the second quarter of the Cougars' 48-17 win over Tulane on Thursday night.
The Houston Chronicle first reported King's diagnosis.
A junior, King has been the linchpin of Houston's offense, the fourth-highest scoring unit in the country. He suffered the non-contact injury after handing the ball off late in the second quarter and carrying out a fake. King grabbed his right knee and fell to the turf immediately afterward and was later carted off. Houston coach Major Applewhite said late Thursday night that King could not straighten out his leg.
King has thrown for 2,982 yards and 36 touchdowns, which is No. 1 in the FBS this season. He has rushed for 674 yards and 14 touchdowns.
The Cougars will likely turn to true freshman Clayton Tune in King's absence next week vs. Memphis. Tune finished Thursday's win in relief of King by completing 6 of 15 passes for 108 yards, two touchdowns and one interception. Houston also has Quinten Dormady, a senior graduate transfer from Tennessee, on its depth chart.