Ryan, 64, was taken to a hospital in Houston from his home in Georgetown, Texas, after experiencing discomfort Sunday. He was scheduled for additional testing Monday, the team said.
"Mr. Ryan is resting comfortably and reports he is feeling better," the Rangers said in a statement. It said Ryan is expected to be released from the hospital in a few days.
Ryan had surgery in 2000 to remove blockage in a heart artery.
Ryan became the team president in February 2008 and after the 2009 season he and Chuck Greenburg bought the team, taking ownership last August. Since then, the Rangers won the 2010 American League pennant and they have won their last 11 games, building a four-game lead in the AL West.
As a player over 27 seasons, Ryan had a 324-292 record with 5,714 strikeouts and seven no-hitters. The strikeout and no-hitter figures are major-league records. He was elected to the Baseball Hall of Fame in 1999.