A new procedure is developed for the estimation of minimum-variance performance bounds in multivariable feedback control systems. The algorithm used in this paper does not require any knowledge of the interactor matrix. Instead: it uses the first few Markov parameters of the plant (up to the delay order of the process) and a set of closed-loop operating data to estimate an expression for the outputs under minimum-variance control. The minimum-variance term of a multivariable feedback control system is shown to be identical to the behavior of the outputs under a finite-horizon minimum-variance control with specified horizon length. The utility of the proposed method in the performance assessment of multivariable control systems is demonstrated through a simulated example.