  An embedding of the Bannai-Ito algebra in the universal enveloping algebra of
$\mathfrak{osp}(1,2)$ is provided. A connection with the characterization of
the little $-1$ Jacobi polynomials is found in the holomorphic realization of
$\mathfrak{osp}(1,2)$. An integral expression for the Bannai-Ito polynomials is
derived as a corollary.
