Two‐fluid theory is used to calculate the nonlinear effect of a finite‐amplitude ion‐cyclotron wave on the simple interchange stability of a magnetically confined plasma. The ion‐cyclotron wave nonlinearly modifies interchange stability through ponderomotive effects and coupling to sidebands of the ion‐cyclotron wave. Nonlinear stability criteria for flute modes are derived. The nonuniformity and polarization of the ion‐cyclotron wave significantly influence the results. A theoretical explanation for recent experimental observations in axisymmetric mirror and tandem mirror plasmas of reduced levels of magnetohydrodynamic activity in the presence of ion‐cyclotron resonant heating remains elusive.