The present study focuses on the semileptonic Bc→Ds*l+l- (l=μ, τ) decay in the standard model (SM) and in the universal extra dimension (UED) model. In addition to the contribution from the flavor changing neutral current (FCNC) transitions the weak annihilation (WA) contribution is also important for this decay. It is found that the WA gives 6.7 times larger branching ratio than the penguin contribution for the decay Bc→Ds*μ+μ-. The contribution from the WA and FCNC transitions are parametrized in terms of the form factors. In this work we first relate the form factors through Ward identities and then express them in terms of g+(0) which is extracted from the decay Bc→Ds*γ through the QCD sum rules approach. These form factors are then used to analyze the physical observables such as branching ratio and helicity fractions of the final state Ds* meson in the SM. This analysis is then extended to the UED model where the dependency of the above mentioned physical observables to the compactification radius R, the only unknown parameter in the UED model, is studied. It is shown that the helicity fractions of Ds* are sensitive to the UED model especially when we have muons as the final state lepton. This sensitivity is marked up at the low q2 region, irrespective of the choice of the form factors. It is hoped that in the next couple of years the LHC will provide enough data on the Bc→Ds*l+l- channel; therefore, these helicity fractions serve as a useful tool to establish new physics predicted by the UED model.