A number of rotation-powered millisecond pulsars are powerful sources of X-ray emission. We present predictions for the spectral characteristics of these sources at gamma-ray energies, using a model for acceleration and pair cascades on open magnetic field lines above the polar caps. Since these pulsars have low surface magnetic fields, the majority do not produce sufficient pairs to completely screen the accelerating electric field allowing particle acceleration to high altitude. The resulting emission above 1 GeV comes from curvature radiation by primary electrons with radiation-reaction-limited Lorentz factors. The spectra are very hard power-laws with exponential cutoffs between 1 and 50 GeV, and the spectral power peaks near the cutoff energy. Millisecond pulsars are thus ideal targets for air-Cherenkov detectors that are able to reach energy thresholds below 50 GeV.