This paper reports measurements of two-pion Bose-Einstein (HBT) correlations in Be+Be collisions at a beam momentum of 150$A\,\mbox{GeV}/\textit{c}$ by the $\mbox{NA61/SHINE}$ experiment at the CERN SPS accelerator. The obtained momentum space correlation functions can be well described by a L\'evy distributed source model. The transverse mass dependence of the L\'evy source parameters is presented, and their possible theoretical interpretations are discussed. The results show that the L\'evy exponent $\alpha$ is approximately constant as a function of $m_{\rm{T}}$ , and far from both the Gaussian case of $\alpha = 2$ or the conjectured value at the critical endpoint, $\alpha = 0.5$. The radius scale parameter $R$ shows a slight decrease in $m_{\rm{T}}$, which can be explained as a signature of transverse flow. Finally, an approximately constant trend of the intercept parameter $\lambda$ as a function of $m_{\rm{T}}$ was observed, different from measurement results at RHIC.
