The advancements of integral inequalities with the help of fractional operators have recently been the focus of attention in the theory of inequalities. In this study, we first review some fundamental concepts, and then using k-conformable fractional integrals, we establish a new integral identity for differentiable functions. Then, considering this identity as an auxiliary result, several Ostrowski-type inequalities are presented for functions whose modulus of the first derivatives are quasi-convex. The obtained results represent generalizations as well as refinements for some published results.