Quessenberry "experienced fatigue and a persistent cough" over the past week, went for a diagnosis and has been placed under the care of M.D. Anderson hospital.
The offensive lineman, drafted in the sixth round in 2013 out of San Jose State, was placed on the Non-Football Injury list.
“Our medical community here in Houston is the best in the world," GM Rick Smith said in a statement. "We are extremely confident in the care and treatment David will receive. He is a fighter and a courageous young man and we look forward to his full and complete recovery. We will continue to support him and his family and look forward to his return to the team."