The critical strength of a magnetic field required for the suppression of the Richtmyer-Meshkov instability (RMI) is investigated numerically by using a two-dimensional single-mode analysis. For the cases of magnetohydrodynamic parallel shocks, the RMI can be stabilized as a result of the extraction of vorticity from the interface. A useful formula describing a critical condition for magnetohydrodynamic RMI is introduced and is successfully confirmed by direct numerical simulations. The critical field strength is found to be largely dependent on the Mach number of the incident shock. If the shock is strong enough, even low-β plasmas can be subject to the growth of the RMI.