Special matrix functions have received substantial attention from a number of domains, including number theory, probability theory, theoretical physics, and the theory of group representations. Lately, mathematical physics and engineering have been greatly influenced by hypergeometric matrix functions and their possible uses. Inspired by the work of matrix analogue of generalized hypergeometric function by Dwivedi and Sahai, and in order to enrich this flourishing field, we introduce a matrix analogue of Mittag-Leffler type confluent hypergeometric function and prove its convergence on \(|z|=1.\) We establish several integral representations, derivative formulas, and finite summation formulas for the Mittag-Leffler type confluent hypergeometric matrix function. Further, we introduce the generalized fractional integral and derivative operators of power functions and obtain the composition formulas with the Mittag-Leffler type confluent hypergeometric matrix function.