White, who started all 31 games for the Cougars in 2019-20, suffered the injury while working out on his own and will undergo surgery later this week.
"I feel badly for Fabian," Sampson said in a statement. "He had worked really hard to have a great senior season. Our thoughts are with him and his family, and we will do all we can to help him recover and have a great senior season in 2021-22."
White has been a key player for the Cougars since arriving on campus as a freshman in 2017-18. He has appeared in 98 career games and increased his scoring and rebounding averages every season on campus, including averaging 9.3 points and 5.5 rebounds as a junior.
It's a notable loss for the Cougars, who are No. 19 in ESPN's Way-Too-Early Top 25 rankings. A pair of Houston's starting guards, Nate Hinton and DeJon Jarreau, are currently testing the NBA draft waters but maintaining their college eligibility.
As a result of the injury, White will redshirt this upcoming season and have one season of eligibility left to use in 2021-22.