We develop an intermolecular potential for the interaction between helium and ammonia including flexibility in the ammonia inversion tunneling coordinate. The potential energy surface is generated by fitting to scaled perturbation theory calculations and is shown to be comparable with high-quality ab initio supermolecule calculations. We have characterized the potential energy surface for a number of ammonia geometries from planar to a highly distorted geometry. For all but the most distorted ammonia geometry, the global minimum has the helium atom in an equatorial location, equidistant from the two closest hydrogen atoms. As the ammonia molecule moves away from the planar configuration, the equatorial minima become less strongly bound while the binding energy increases in the axial regions of the potential energy surface. At the most distorted ammonia geometry, the equatorial minimum is a local minimum, and the global minimum has the helium atom on the symmetry axis of the molecule at the hydrogen end.