We present the Model-Agnostic Dark Halo Analysis Tool (MADHAT), a numerical tool which implements a Fermi-LAT data-driven, model-independent analysis of gamma-ray emission from dwarf satellite galaxies and dwarf galaxy candidates due to dark matter annihilation, dark matter decay, or other nonstandard or unknown astrophysics. This tool efficiently provides statistical upper bounds on the number of observed photons in excess of the number expected, based on empirical determinations of foregrounds and backgrounds, using a stacked analysis of any selected set of dwarf targets. It also calculates the resulting bounds on the properties of dark matter under any assumptions the user makes regarding dark sector particle physics or astrophysics. As an application, we determine new bounds on Sommerfeld-enhanced dark matter annihilation in a set of eight dwarfs. MADHAT v1.0 includes 58 dwarfs and dwarf candidate targets, and we discuss future planned developments. MADHAT is available and will be maintained at https://github.com/MADHATdm.