We study the galaxy bispectrum multipoles in the Hu-Sawicki $f(R)$ gravity model, where a scalar degree of freedom mediates a fifth force that is screened in high-density environments. The model is specified by $f_{R0}$, the present-day background value of the scalar field, which controls the strength of deviations from general relativity. Using perturbation theory, we compute the redshift-space galaxy bispectrum with the full scale- and time-dependent second-order kernels, incorporating corrections from the scale-dependent growth rate and nonlinear screening. Expanding the bispectrum in spherical harmonics, we analyze the sensitivity of the multipoles to modified gravity and forecast their detectability in a Euclid-like survey. The monopole ($B_0^0$) and quadrupole ($B_2^0$) show the strongest signatures, with relative deviations of 2%–8% at $z=0.7$ and $k_1\simeq 0.3h{\mathrm{Mpc}}^{-1}$ (largest side of the triangle) for $f_{R0}={10}^{-5}$. Higher multipoles provide weaker but complementary signals. For Euclid, we forecast signal-to-noise ratios up to $\sim 30$ for the monopole and $\sim 15$ for the quadrupole including the finger-of-God damping and shot noise effect. These results demonstrate that bispectrum multipoles are a powerful probe of gravity, capable of breaking degeneracies with bias and velocity effects and strengthening constraints on deviations from $\mathrm{\Lambda }\mathrm{CDM}$.

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• Cosmological parameters
• Evolution of the Universe
• Large scale structure of the Universe