We have performed a search for the rare leptonic decay B+-->mu(+)nu(mu) with data collected at the Upsilon(4S) resonance by the BABAR experiment at the PEP-II storage ring. In a sample of 88.4 x 10(6) BB pairs, we find no significant evidence for a signal and set an upper limit on the branching fraction B(B+-->my(+)nu(my))< 6.6 x 10(-6) at the 90% confidence level.