We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the light quarks that induce the pion mean field and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of model-independent relations and calculate the heavy-baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the baryon is predicted.