We investigate the mass-velocity dispersion relation (MVDR) in 29 galaxy clusters in the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS). We measure the spatially resolved, line-of-sight velocity dispersion profiles of these clusters, which we find to be mostly flat at large radii, reminiscent of the rotation curves of galaxies. We discover a tight empirical relation between the baryonic mass M bar and the flat velocity dispersion σ of the member galaxies, i.e., MVDR,, with the lognormal intrinsic scatter of 12 -3 +3. The residuals of the MVDR are uncorrelated with other cluster properties like temperature, cluster radius, baryonic mass surface density, and redshift. These characteristics are reminiscent of the MVDR for individual galaxies, albeit at about a ten times larger characteristic acceleration scale. The cluster baryon fraction falls short of the cosmic value, exposing a problem: the discrepancy increases systematically for clusters of lower mass and lower baryonic acceleration.