Inmate Michael Vaisa fell Saturday afternoon in a housing unit in the Jameson Annex in Sioux Falls.
The 45-year-old was taken to a hospital for treatment of head and neck injuries and placed on life support, but he died Wednesday.
The state says witnesses reported seeing Vaisa fall from the second floor of the housing unit to the first floor because of a medical condition. Details were not released.
The Division of Criminal Investigation is investigating and an autopsy will be done.
Vaisa was serving a life sentence for first-degree murder and first-degree burglary out of New Mexico under an interstate compact agreement.