Using a sample of 2.25 x 10(8) J/psi events collected with the BESIII detector at the BEPCII collider, we search for the J/psi semileptonic weak decay J/psi -> D-s(-) e(+)nu(e) +c.c. with a much higher sensitivity than previous searches. We also perform the first search for J/psi -> D-s(*-) e(+) nu(e) + 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/psi -> D-s(-) e(+) nu(e) + c.c.) < 1.3 x 10(-6) and B(J/psi -> D-s*(-) e(+) nu(e) + c.c.) < 1.8 x 10(-6), respectively. Both are consistent with Standard Model predictions.