He wore an Indians jersey with the No. 50, to celebrate the golden anniversary of his historic space flight on Feb. 20, 1962, when he became the first American to orbit the Earth.
"It seems like it was two or three weeks ago," the 91-year-old Glenn said before delivering an underhanded toss from the mound to Indians coach Sandy Alomar Jr.
Prior to his throw, Glenn asked the crowd for a moment of silence to honor Neil Armstrong, the first man to walk on the moon, who died Saturday at age 82.
"Neil was a true patriot and American hero," said Glenn, with wife Annie at his side.
He went on to detail Armstrong's numerous accomplishments, which included flying combat missions in Korea and becoming a record-setting test pilot before joining the space program.
Glenn said he swelled with pride when Armstrong landed on the moon on July 20, 1969. He said his only regret was that it wasn't him.
"I told Neil at the time, 'By nature I'm not a jealous man, but in your case I'll make an exception.' " said Glenn, who went on to become a U.S. Senator in his native Ohio.
Glenn's baseball heroes when he was young were Hall of Famers Bob Feller and Earl Averill of the Indians as well as Hank Greenberg of the Detroit Tigers.
He said getting paired up as pilots with Hall of Famer Ted Williams was a thrill. Glenn and Williams flew several missions together during the Korean War.
"Ted was a great wing man, though he didn't like to fly on instruments," Glenn said. "He took two hits during the war and was lucky to survive."
Glenn described the time that Williams refused to eject from the cockpit and landed his plane while it was on fire.
"He was a dedicated American and terrific pilot," Glenn said.