<p>Modified gravity theories offer a well-motivated extension of General Relativity and provide a possible explanation for the late-time accelerated expansion of the Universe. Among them, <i>f</i>(<i>R</i>) gravity represents a minimal and theoretically appealing class, characterized by the Compton wavelength parameter <i>B</i>₀, which quantifies deviations from General Relativity. In this work, we explore the capability of future neutral hydrogen (HI) 21-cm intensity mapping (IM) observations to constrain <i>f</i>(<i>R</i>) gravity at low redshifts. We perform Fisher-matrix forecasts for <i>B</i>₀ and standard cosmological parameters using upcoming 21-cm IM experiments, including BINGO and SKA1-MID (Band 1 and Band 2), both individually and in combination with Planck cosmic microwave background (CMB) priors. For the phenomenological HI treatment, we obtain <i>σ</i>(<i>B</i>₀) = 3.73 × 10⁻⁶, 5.98 × 10⁻⁶, and 6.78 × 10⁻⁸ for BINGO, SKA1-MID Band 1, and Band 2, respectively, and the tightest bound is improved to 3.95 × 10⁻⁸ when Planck priors are included. We further consider a redshift-dependent HI model with fixed Ω_HI(<i>z</i>) and <i>b</i>_HI(<i>z</i>), and find that the constraints remain of similar order, confirming the robustness of the results. In both cases, SKA1-MID Band 2 provides the strongest sensitivity, while foreground residuals degrade the constraints but do not change the main conclusion that future HI intensity mapping, especially combined with CMB data, can provide stringent tests of General Relativity on cosmological scales.</p>