His death was initially confirmed to the Daily Journal by legislative colleagues and later announced in a statement from UMMC.
Colleagues said Turner, 64, had suffered from a brain tumor.
Turner was first elected to the Senate in 1992. An attorney, he formerly chaired the Senate Judiciary Committee and in the current term chaired the chamber's Ethics Committee.
Sen. Hob Bryan told The Associated Press Turner championed public education and was an "extraordinarily beloved and respected" senator.