Using (10087 ± 44) × 106 J/ψ events collected with the BESIII detector at the BEPCII e + e − storage ring at the center-of-mass energy of s = 3.097 GeV, we present a search for the rare semi-muonic charmonium decay J/ψ → D − μ + νμ + c.c. Since no significant signal is observed, we set an upper limit of the branching fraction to be B (J/ψ → D − μ + νμ + c.c.) < 5.6 × 10−7 at 90% confidence level. This is the first search for the weak decay of charmonium with a muon in the final state. [Figure not available: see fulltext.].