The concept of a Prüfer ring is generalized to orders in simple Artinian rings so that the new concept gives a minimal class of rings closed under Morita equivalence, but in the commutative case does not extend the class of Prüfer domains. In §1 this problem is solved and some elementary properties of noncommutative Prüfer rings are given. In §2 theorems on the localization of a noncommutative Prüfer ring with respect to a prime ideal are proved, these being the basis of the theory. In §3 noncommutative Prüfer rings in a simple finite-dimensional algebra over a field are considered. The main problem, which is posed and partially solved here, involves the connection between a noncommutative Prüfer ring and its center.