The 85-year-old former senator and his 86-year-old wife, Annie, are in fair condition at a hospital in Columbus.
Both were being evaluated in the emergency room and were "extremely stable," the nursing supervisor told The Columbus Dispatch early Saturday morning.
Police said their car collided with another Friday night on the northeast side of Columbus.
The driver of the other car told The Dispatch that she was headed east and Glenn was driving west. Amy Myers said her car and Glenn's collided as he tried to turn left onto a ramp for Interstate 270.
Sen. Glenn was "very sincerely sorry," Myers said.
Glenn was the first American to orbit the earth in 1962. He served in the Senate from 1974 to 1998, and went back into space in 1998, at the age of 77.