Josephson current between two superconductors provides a phase sensitive tool for probing their pairing symmetries. Here we fabricate and study experimentally high-quality Josephson junctions between a conventional s-wave superconductor Nb and a multi-band iron-pnictide Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. Junctions exhibit a large enough critical current density to preclude the d-wave symmetry of the order parameter in the pnictide. However, the $I_cR_n$ product is very small $simeq 3~mu$V, which is not consistent with the sign-preserving $s_{++}$ symmetry either. We argue that the small $I_cR_n$ value along with its unusual temperature dependence provide evidence for the $s_{pm}$ symmetry of the order parameter in Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. We conclude that it is the phase sensitivity of our junctions that leads to an almost complete (bellow a sub-percent) cancellation of opposite supercurrents from the sign-reversal $s_{pm}$ bands in the pnictide.