  The ratio of branching fractions between $B^{0} \rightarrow J/\psi \pi^{0}$
and $B^{+} \rightarrow J/\psi K^{*+}$ decays is measured with proton-proton
collision data collected by the LHCb experiment, corresponding to an integrated
luminosity of 9 fb$^{-1}$. The measured value is $\frac{\mathcal{B}_{B^{0}
\rightarrow J/\psi \pi^{0}}}{\mathcal{B}_{B^{+} \rightarrow J/\psi K^{*+}}} =
(1.153 \pm 0.053 \pm 0.048 ) \times 10^{-2}$, where the first uncertainty is
statistical and the second is systematic. The branching fraction for $B^{0}
\rightarrow J/\psi \pi^{0}$ decays is determined using the branching fraction
of the normalisation channel, resulting in $\mathcal{B}_{B^{0} \rightarrow
J/\psi \pi^{0}} = (1.670 \pm 0.077 \pm 0.069 \pm 0.095) \times 10^{-5}$, where
the last uncertainty corresponds to that of the external input. This result is
consistent with the current world average value and competitive with the most
precise single measurement to date.
