Many star-forming galaxies and those hosting active galactic nuclei show evidence of massive outflows of material in a variety of phases including ionized, neutral atomic, and molecular. Molecular outflows in particular have been the focus of recent interest as they may be responsible for removing gas from the galaxy, thereby suppressing star formation. As material is ejected from the cores of galaxies, interactions of the outflowing material with the interstellar medium can accelerate cosmic rays and produce high-energy gamma rays. In this work, we search for gamma-ray emission from a sample of local galaxies known to host molecular outflows using data collected by the Fermi Large Area Telescope. We employ a stacking technique in order to search for and characterize the average gamma-ray emission properties of the sample. Gamma-ray emission is detected from the galaxies in our sample at the 4.4σ level with a power-law photon index of Γ ≈ 2 in the 1–800 GeV energy range. The emission is found to correlate with tracers of star formation activity, namely the 8–1000 μm infrared luminosity. We also find that the observed signal can be predominantly attributed to H ii galaxies hosting energy-driven outflows. While we do not find evidence suggesting that the outflows are accelerating charged particles directly, galaxies with molecular outflows may produce more gamma rays than galaxies without outflows. In particular, the set consisting of gamma-ray-detected galaxies with molecular outflows are nearly perfect calorimeters and may be future targets for searches of high-energy neutrinos.