The team announced that Quessenberry experienced fatigue and a persistent cough over the past week and was diagnosed after seeking a medical evaluation to find out the cause.
"Im gonna kick the crap outta this thing and come back even stronger! I will win this fight!" Quessenberry told CSN Houston.
O'Brien added: "We want everybody to know, especially David Quessenberry, that we're very much in David Quessenbery's corner."
A sixth-round pick in 2013, Quessenberry missed all of last season with a broken foot.
UPDATE: Quessenberry addressed his illness Tuesday on Twitter: