Germanium nanomembranes are suitable for flexible electronics, including high-mobility nonsilicon transistors, fast radio-frequency switches, microwave diodes, and high-performance photodetectors. In order to enhance the flexibility of the germanium-based devices, we present a strategy to integrate single-crystalline germanium nanomembranes into a wave-like wrinkled geometry with a uniform periodicity and amplitude on elastomeric substrates. Wrinkled single-crystalline germanium nanomembranes are realized with a reversible and large deformation up to 10%, and the stretchable metal-germanium-metal photodetectors have been demonstrated. Optoelectronic response studies reveal that the wrinkled germanium-based photodetectors exhibit enhanced efficiency of optoelectronic interactions compared with planar photodetectors using flat germanium nanomembranes. Furthermore, the wrinkled photodetectors reveal high response speed and stretchable capability of up to 8.56%. This paper may pave the way for the integration of germanium nanomembranes into the field of flexible/wearable optoelectronics.