  Dark matter annihilation in dwarf spheroidal (dSph) galaxies near the Milky
Way has the potential to produce a detectable signature in gamma-rays. The
amplitude of this signal depends on the dark matter density in a dSph, the dark
matter particle mass, the number of photons produced in an annihilation, and
the possibly velocity-dependent dark matter annihilation cross section. We
argue that if the amplitude of the annihilation signal from multiple dSphs can
be measured, it is possible to determine the velocity-dependence of the
annihilation cross section. However, we show that doing so will require
improvements in constraints on the dSph density profiles. Making reasonable
assumptions about these improvements, we make forecasts for the ability of
current and future experiments -- including Fermi, CTA and AMEGO -- to
constrain the dark matter annihilation velocity dependence.
