The man had been housed in the medical facility and when staff went to check on him, they found he wasn't breathing.
Medics were called to the scene but attempts to revive the inmate were not successful.
Officials did not give a cause of death and are still investigating the incident. The inmate's name was not released.
Two other inmates have died at the facility in the past year. William Williams, 59, died in jail on the night of Sept. 14 after jail staff Tased and put him in an isolation cell.
And in July, a 22-year-old inmate died after reportedly suffering an allergic reaction to milk.