Using a sample of 2.25×108 J/ψ events collected with the BESIII detector at the BEPCII collider, we search for the J/ψ semileptonic weak decay J/ψ→Ds−e+νe+c.c. with a much higher sensitivity than previous searches. We also perform the first search for J/ψ→Ds*−e+νe+c.c. No significant excess of a signal above background is observed in either channel. At the 90% confidence level, the upper limits are determined to be B(J/ψ→Ds−e+νe+c.c.)<1.3×10−6 and B(J/ψ→Ds*−e+νe+c.c.)<1.8×10−6, respectively. Both are consistent with Standard Model predictions.