The court's decision means Hill will not likely be scheduled for execution before the state's current supply of a lethal injection drug expires next week.
Hill was one of two inmates scheduled to be executed this week. The other was also granted a stay, although the state has appealed that.
Hill was convicted in the 1990 beating death of fellow inmate Joseph Handspike. Hill was serving a life sentence at the time for the killing of his girlfriend.
While Hill's lawyer argues he is mentally disabled, the state says the defense failed to meet its burden of proving that beyond a reasonable doubt.