Massive protostars have associated bipolar outflows with velocities of hundreds of km s-1. Such outflows can produce strong shocks when they interact with the ambient medium leading to regions of nonthermal radio emission. Aims. We aim at exploring under which conditions relativistic particles are accelerated at the terminal shocks of the protostellar jets and whether they can produce significant gamma-ray emission. Methods. We estimate the conditions necessary for particle acceleration up to very high energies and gamma-ray production in the nonthermal hot spots of jets associated with massive protostars embedded in dense molecular clouds. Results. We show that relativistic bremsstrahlung and proton-proton collisions can make molecular clouds with massive young stellar objects detectable by the Fermi satellite at MeV-GeV energies and by Cherenkov telescope arrays in the GeV-TeV range. Conclusions. Gamma-ray astronomy can be used to probe the physical conditions in star-forming regions and particle acceleration processes in the complex environment of massive molecular clouds.