We present an a posteriori error analysis for the mixed virtual element method (mixed-VEM) applied to general second order elliptic equations. The resulting error estimator is of residual-type. Via the inclusion of a fully local postprocessing of the mixed-VEM solution, we show that the estimator provides a reliable and efficient control on the L2-norm error between the exact and the postprocessed flux. Numerical examples confirm the theoretical properties of the estimator, and show that it can be effectively used to drive an adaptive mesh refinement algorithm.