A thickness dependent exchange bias in the low temperature martensitic state of epitaxial Ni-Mn-Sn thin films is found. The effect can be retained down to very small thicknesses. For a Ni50Mn32Sn18 thin film, which does not undergo a martensitic transformation, no exchange bias is observed. Our results suggest that a significant interplay between ferromagnetic and antiferromagnetic regions, which is the origin for exchange bias, is only present in the martensite. The finding is supported by ab initio calculations showing that the antiferromagnetic order is stabilized in the phase.