This technical note investigates the model reduction problem for mean square stable discrete time Markov jump linear systems. For this class of systems a balanced truncation algorithm is developed. The reduced order model is suboptimal, however the approximation error, which is captured by means of the stochastic L-2 gain, is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode. Such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view.