The development of methods for controlling the motion and arrangement of molecules adsorbed on a metal surface would provide a powerful tool for the design of molecular electronic devices. Recently, metal phthalocyanines (MPc) have been extensively considered for use in such devices. Here we show that applied electric fields can be used to turn off the diffusivity of iron phthalocyanine (FePc) on Au(111) at fixed temperature, demonstrating a practical and direct method for controlling and potentially patterning FePc layers. Using scanning tunneling microscopy, we show that the diffusivity of FePc on Au(111) is a strong function of temperature and that applied electric fields can be used to retard or enhance molecular diffusion at fixed temperature. Using spin-dependent density-functional calculations, we then explore the origin of this effect, showing that applied fields modify both the molecule-surface binding energies and the molecular diffusion barriers through an interaction with the dipolar Fe-Au adsorption bond. On the basis of these results FePc on Au(111) is a promising candidate system for the development of adaptive molecular device structures.