The team said Tuesday that the 23-year-old Quessenberry had a persistent cough over the past week and was tired, prompting him to seek an evaluation. He is being treated at a Houston-area hospital.
The 6-5, 300-pound Quessenberry is a second-year pro from San Jose State. Houston drafted him with the eighth pick of the sixth round (No. 176 overall) in the 2013 draft and he was signed a month later.
Texans general manager Rick Smith called Quessenberry ''a fighter and a courageous young man and we look forward to his full and complete recovery.''