We report a search for narrow resonances, produced in p p̄ collisions at √ s=1.96 TeV, that decay into muon pairs with invariant mass between 6.3 and 9.0 GeV/c 2. The data, collected with the CDF II detector at the Fermilab Tevatron collider, correspond to an integrated luminosity of 630 pb -1. We use the dimuon invariant mass distribution to set 90% upper credible limits of about 1% to the ratio of the production cross section times muonic branching fraction of possible narrow resonances to that of the Υ(1S) meson. © 2009 Springer-Verlag.