While about 20 Type II supernova progenitors have been identified using optical data from the Hubble Space Telescope (HST), direct detection of type Ib/Ic supernova (SN Ib/Ic) progenitors remains challenging due to their faint optical brightness and highly obscured environments. This study aims to investigate the detection limits and advantages of near-infrared (near-IR) observations with the James Webb Space Telescope (JWST) and the Nancy Grace Roman Space Telescope (NGRST) for the detection of SN Ib/Ic progenitors. The spectral energy distributions of SN Ib/Ic progenitor models with various masses, chemical compositions, and mass-loss rates are calculated with the non-LTE radiative transfer code CMFGEN. We then assess the detectability of SN Ib/Ic progenitors using near-IR filters from the JWST and the NGRST, comparing the results to the capabilities of the HST. Our analysis indicates that near-IR observations significantly outperform the HST in detecting SN Ib/Ic progenitors when considering the effect of extinction. Near-IR magnitudes also provide better constraints on the mass-loss rates of progenitors because of the free-free emission from the wind matter. Additionally, near-IR magnitudes and color-color diagrams are effective in distinguishing SN Ib/Ic progenitors from possible companion and/or background objects. This study suggests that the JWST and the NGRST can play a crucial role in advancing our understanding of SN Ib/Ic progenitors by improving detectability and offering better constraints on progenitor properties. We emphasize that observations with exposure times exceeding 1 hour would be needed to detect typical SNe Ib/Ic progenitors at distances greater than 10 Mpc.