  Addition of boundary localised kinetic and Yukawa terms to the action of a
5-dimensional Standard Model would non-trivially modify the Kaluza-Klein
spectra and some of the interactions among the Kaluza-Klein excitations
compared to the minimal version of this model, in which, these boundary terms
are not present. In the minimal version of this framework known as Universal
Extra Dimensional model, special assumptions are made about these unknown,
beyond the cut-off contributions to restrict the number of unknown parameters
of the theory to a minimal. We estimate the contribution of Kaluza-Klein modes
to the branching ratios of $B_{s(d)}\rightarrow\mu^{+}\mu^{-}$ in the framework
of non-minimal Universal Extra Dimensional, at one loop level. The results have
been compared to the experimental data to constrain the parameters of this
model. From the measured decay branching ratio of $B_s \rightarrow \mu^+ \mu^-$
(depending on the values of boundary localised parameters) lower limit on
$R^{-1}$ can be as high as 800 GeV. We have briefly reviewed the bounds on
nmUED parameter space coming from electroweak precision observables. The
present analysis ($B_s \rightarrow \mu^+ \mu^-$) has ruled out new regions of
parameter space in comparison to the analysis of electroweak data. We have
revisited the bound on $R^{-1}$ in Universal Extra Dimensional model, which
came out to be 454 GeV. This limit on $R^{-1}$ in Universal Extra Dimensional
framework is not as competitive as the limits derived from the consideration of
relic density or Standard Model Higgs boson production and decay to $W^+ W^-$.
Unfortunately, $B_{d}\rightarrow\mu^{+}\mu^{-}$ decay branching ratio would not
set any significant limit on $R^{-1}$ in a minimal or non-minimal Universal
Extra Dimensional model.
