Efficient excitonic solar cells preferably require materials with an optical gap in the near-infrared region and high absorption coefficients. Additionally, it is well-known that heterostructures open the possibility of tailoring device properties by taking advantage of the characteristics of individual materials, so that new practical applications can arise. Regarding these ingredients, we propose that the recent synthesized monolayer MoTe2 and the InN compound seem to favorably fit into this category. We carry out ab initio density functional theory calculations to study the electronic and optical properties of heterostructures based on MoTe2 and InN monolayers. Our results indicate that one of the most stable heterostructures presents type-II band alignments and photoexcited states in the energy range of 1.1-1.3 eV, where power conversion efficiency reaches its maximum. We also propose a prototypical device based on these materials and study their potential as excitonic solar cells. In doing so, we show that heterostructures based on MoTe2-InN are able to combine the near-infrared absorption of MoTe2 together with the low refractive index and high absorbance of InN to give rise to improved optical properties such as the formation of photoexcited states with lower binding energies, when compared with the individual monolayers, long exciton lifetimes in the nanosecond scale, as well as high power density ratios. These overall results point toward the potential of MoTe2-InN heterostructures for photovoltaic applications.