[en] The effect of a beam-beam interaction on the motion of a circulating beam in a 50 GeV x 50 GeV muon-collider ring is investigated by weak-stron beam modeling. In the present design of the muon-collider storage ring, the frequency-slippage factor η₁ is approximately -5 x 10^-7 so that the synchrotron motion is nearly frozen. This may lead to an increase in the energy spread due to the beam-beam interaction. Through the weak-strong beam modeling, we have investigated the parametric dependencies of the energy spread induced by the beam-beam interaction. We show in this paper that the energy spread due to the beam-beam interaction is large and can be compensated for by employing one rf cavity in the ring with a modest rf voltage. (author)