According to a statement from his agents, Quessenberry thought he was having a persistent chest cold, but the lymphoma diagnosis came last week after he had shortness of breath during team practice.
Quessenberry is currently being treated at M.D. Anderson Hospital in Houston.
"Our medical community here in Houston is the best in the world," Texans general manager Rick Smith said. "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."
The tackle is also optimistic he will make a speedy recovery.
"I'm gonna kick the crap outta this thing and come back even stronger! I will win this fight!" Quessenberry told CSN Houston.
Quessenberry was the Texans' sixth-round pick in 2013 and missed all of last season with a broken foot.