Dwarf spheroidal galaxies are among the most important targets in the search for gamma rays from dark matter annihilation in the cosmos. In fact, joint likelihood analyses using dozens of dwarfs have recently reached the sensitivity necessary to test the putative dark matter signal detected from the Galactic center. While the gamma-ray flux from conventional astrophysical emission processes in dwarfs is generally assumed to be negligible, these backgrounds have not been previously quantified. Understanding possible backgrounds will be essential if a signal is detected, as we have seen in the case of the Galactic center. We present an estimate of the expected gamma-ray signal produced by millisecond pulsars in 30 dwarf spheroidal galaxies. We predict that millisecond pulsars in the most massive classical dwarfs produce a gamma-ray flux within an order of magnitude of the current Fermi Large Area Telescope sensitivity for individual targets. Moreover, we estimate the millisecond pulsar emission in the ultra-faint dwarfs most important for dark matter searches to be more than an order of magnitude below current upper limits.