Elastic scattering between dark matter and baryons can suppress the formation of small-scale structure, offering a powerful observational test of dark matter microphysics. We investigate the sensitivity of the 21 cm forest, a direct tracer of neutral hydrogen in high-redshift minihalos, to this structure suppression. Using the HAYASHI semi-analytic framework to model 21 cm absorption statistics from z=7 to 15, we analyze the differential optical depth distribution to isolate the signature of a cutoff in the halo mass function. Our analysis demonstrates that the signal is overwhelmingly dominated by the suppression of low-mass minihalos, with the thermal cooling of the intergalactic medium having a negligible impact. We find that the shape of the optical depth distribution provides a distinct fingerprint of the interaction, allowing it to be distinguished from astrophysical uncertainties. Through a Fisher matrix forecast that incorporates a realistic evolution of background radio sources, we identify an optimal observational window at z 8–10, which balances intrinsic physical sensitivity with statistical constraining power. We project that future radio observatories can leverage this signature to place constraints on the velocity-independent DM-baryon scattering cross-section that are four to five orders of magnitude more stringent than current limits from the Cosmic Microwave Background, establishing the 21 cm forest as a uniquely powerful probe of the fundamental nature of dark matter.