We investigate emergent superconductivity and non-reciprocal transport (magnetochiral anisotropy, superconducting diode effect) at the heterointerface of two non-superconducting van der Waals (vdW) materials, the Dirac semimetal ZrTe₂ and the antiferromagnetic iron chalcogenide FeTe, grown using molecular beam epitaxy. We show from electrical transport measurements that two-dimensional (2D) superconductivity arises at the heterointerface below a critical temperature T_c ∼ 10~K. In the superconducting transition region, non-reciprocal transport, characterized by the magneto-chiral anisotropy, exhibits a magnitude comparable to that observed in topological insulators, and is enhanced by a factor of three when the heterostructure is capped with a 2D vdW ferromagnet (CrTe₂). Below T_c, the superconducting diode effect exhibits an efficiency of 29%. With strong spin-orbit coupling in ZrTe₂, these epitaxial heterostructures provide an attractive epitaxial vdW platform for exploring unconventional superconductivity in Dirac semimetals and for developing non-reciprocal devices for superconducting electronics.