Pulsars emerge in the Fermi era as a sizable population of gamma-ray sources. Millisecond pulsars (MSPs) constitute an older subpopulation whose sky distribution extends to high Galactic latitudes, and it has been suggested that unresolved members of this class may contribute a significant fraction of the measured large-scale isotropic gamma-ray background (IGRB). We investigate the possible energy-dependent contribution of unresolved MSPs to the anisotropy of the Fermi-measured IGRB. For observationally motivated MSP population models, we show that the preliminary Fermi anisotropy measurement places an interesting constraint on the abundance of MSPs in the Galaxy and the typical MSP flux, about an order of magnitude stronger than constraints on this population derived from the intensity of the IGRB alone. We also examine the possibility of an MSP component in the IGRB mimicking a dark matter signal in anisotropy-based searches, and conclude that the energy dependence of an anisotropy signature would distinguish MSPs from all but very light dark matter candidates.