Ryan, who also is the club's chief executive and president, is to rest at home in Georgetown for several days before returning to work.
The 64-year-old Hall of Fame pitcher was hospitalized in Houston after experiencing discomfort early Sunday at his home. He underwent a series of precautionary tests Monday and the Rangers said the results showed no new developments with his previous heart condition.
He is to continue to be treated with medication.
Ohio bar shooting arrested, charged with murder
Beautician charged with giving client fatal silicone butt injection