We investigate the influence of the film thickness on the martensitic transformation for the example of Ni-Mn-Sn thin films. Epitaxial films with thicknesses ranging from 100 nm down to 10 nm were deposited on MgO by co-sputtering on heated substrates. The martensitic transformation is investigated using temperature dependent x-ray diffraction, magnetization and resistivity measurements. X-ray diffraction and transmission electron microscopy is used to study the growth and the martensitic structure of the films. We find that the martensitic transformation temperatures reduce and the transformation range increases with decreasing film thickness. We show that the transformation is still possible down to a film thickness of 10 nm. A systematic study on the resistance change caused by the martensitic transformation implies that the transformation is suppressed close to the interfaces to the MgO.