His daughter says the 89-year-old former U.S. senator fell outside of the Dakota Wesleyan University's McGovern Library in Mitchell, which is across the street from one of his homes.
A school official said McGovern hit his head on the pavement about two hours before he was scheduled to appear on a live C-SPAN interview at the library. Witnesses say McGovern was bleeding profusely but remained conscious and talking.
"Senator McGovern is alert and resting comfortably but, as with any head injury, it is important that we observe the situation closely," said Dr. Michael Elliott in a written statement Saturday.
The statement said McGovern was in stable condition, though no other details were released. The hospital said his family was asking for privacy.
The Associated Press contributed to this story.
