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We fabricated and tested InN nanopyramid based photodetectors designed for operation in the telecommunication-wavelength range. We found that the spectral sensitivity of InN photodetectors can be engineered by their size and by the strain interaction with the masked SiO2/GaN substrates. The band edge luminescence energy of the InN nanopyramids depends linearly on the structure size. Furthermore, InN nanopyramid based photodetectors exhibit a low device RC constant, low dark currents below 1 nA, as well as a responsivity of ~ 0.2 A/W at 1550 nm wavelength. InN nanopyramid based photodetectors are very promising candidates for high-speed optoelectronics within the telecommunication wavelength range.