We present the first systematic study of explosive dispersal outflows (EDOs) as potential sources of high-energy emission in the Milky Way. EDOs are energetic outflows produced during dynamical interactions in young, massive star-forming regions, and their physical conditions make them promising environments for cosmic-ray acceleration. Using 16 yr of 0.2–500 GeV Fermi-Large Area Telescope observations, we study theγ-ray properties of seven EDOs. Three EDOs, DR21, G34.26+0.15, and G5.89−0.39, show spatially coincident GeV emission, while the remaining systems yield nondetections. Among the sample, DR21 stands out as the brightest candidate, with a detection significance ≥40σ. Its spectrum is well described by a power law with an exponential cutoff, and the integrated luminosity in the 0.1–500 GeV band isL_γ≃2×10³⁵erg s⁻¹. When compared with the outflow’s estimated kinetic energy, the inferred cosmic-ray acceleration efficiency is ≤15%, consistent with values for shocks in dense molecular environments. The energetics and morphology support an association between the DR21 molecular outflow and the observedγ-rays. Our results demonstrate that EDOs span a wide range ofγ-ray luminosities and efficiencies, suggesting they may contribute to the Galactic cosmic-ray budget. This motivates searches for additional EDOs and improved multiwavelength characterization of their environments.