Tunable surface morphology in III-V semiconductor nanomembranes provides opportunities to modulate electronic structures and light interactions of semiconductors. Here, we introduce a vacuum-induced wrinkling method for the formation of ordered wrinkles in InGaAs nanomembranes (thickness, 42 nm) on PDMS microwell arrays as a strategy for deterministic and multidirectional wrinkle engineering of semiconductor nanomembranes. In this approach, a vacuum-induced pressure difference between the outer and inner sides of the microwell patterns covered with nanomembranes leads to bulging of the nanomembranes at the predefined microwells, which, in turn, results in stretch-induced wrinkle formation of the nanomembranes between the microwells. The direction and geometry of the nanomembrane wrinkles are well controlled by varying the PDMS modulus, depth, and shape of microwells, and the temperature during the transfer printing of nanomembrane onto heterogeneous substrates. The wrinkling method shown here can be applied to other semiconductor nanomembranes and may create an important platform to realize unconventional electronic devices with tunable electronic properties.