Bryant, who was given medication by the Cowboys' doctors, was sleeping and unavailable for comment Tuesday afternoon.
Tuesday's practice was closed to the media, and so is Wednesday's.
Jones, at the NFL owners meetings Tuesday in Irving, Texas, was asked if thought Bryant would return to practice Wednesday.
"I do, and we basically told him to stay home and be there tomorrow [Wednesday]," Jones said, adding that Bryant first felt ill Monday. "Flu, upset stomach yesterday, and the trainers who saw him yesterday told him to stay home."
Bryant, the Cowboys' first-round draft pick, battled fatigue on the first day of the rookie minicamp at the end of April. He was coughing up water and bent over, but he was fine the next two days of the minicamp.