In an emailed statement, the family said Cannon, 75, "is alert and resting."
"He did have a stroke and the doctors will conduct tests to see the extent. They will keep him in ICU tonight and watch him overnight," the statement said. "The family thanks everyone for their prayers and concerns."
Cannon was transported by ambulance from the state penitentiary at Angola at about 12:30 p.m., said Cathy Fontenot, a spokeswoman for the prison.
Cannon has been director of the prison's dental program for about 15 years.
He won the 1959 Heisman Trophy after starring at LSU. He went on to a successful pro career in the American Football League with the Houston Oilers and Oakland Raiders, and after football went to dental school.
In 1983, Cannon was arrested on federal counterfeiting charges. He ultimately pleaded guilty, served half of a five-year sentence and came out broke. Though tarnished for a time, Cannon's reputation has been rebuilt through his work at the penitentiary, where he tries to serve as a positive example for inmates, and through his routine participation in LSU events.
Information from: The Advocate, http://theadvocate.com