Dynamic manipulation of optoelectronic responses by mechanical stimuli is promising for developing wearable electronics and human-machine interfacing. Although 2D-3D hybrid heterostructures can bring advancements in optoelectronics, their dynamic optical responses to external strains remain rarely studied. Here, we demonstrate the strain-tuned recombination dynamics of monolayer-MoS2 and thin-film-GaN heterostructures. We find that optical excitons in the heterostructures, apart from trions, can be markedly modulated by strains. We argue that MoS2 piezoelectric dipoles across the interfaces lead to curved band diagrams, in which optical excitons dissociate into spatially separated quasi-particles and concurrently relocate to the maxima of valence bands and the minima of conduction bands. With the increase in tensile strains, the photoluminescence (PL) intensity of the heterostructures shows quenched responses. Noticeably, the change in PL spectra strongly depends on the directions of the applied strains because of the lateral piezoelectric periodicity of MoS2 flakes. This work not only helps in understanding the underlying physics of the decreased PL intensities upon applying strains but also demonstrates a feasible way (i.e., strains) to manipulate the PL efficiency of 2D-material-based optoelectronics.