We use large-volume N-body simulations to predict the clustering of dark matter in redshift space in f(R) modified gravity cosmologies. This is the first time that the non-linear matter and velocity fields have been resolved to such a high level of accuracy over a broad range of scales in this class of models. We find significant deviations from the clustering signal in standard gravity, with an enhanced boost in power on large scales and stronger damping on small scales in the f(R) models compared to general relativity (GR) at redshifts z < 1. We measure the velocity divergence (Pθθ) and matter (Pδδ) power spectra and find a large deviation in the ratios and Pδθ/Pδδ between the f(R) models and GR for 0.03 < k/(h Mpc−1) < 0.5. In linear theory, these ratios equal the growth rate of structure on large scales. Our results show that the simulated ratios agree with the growth rate for each cosmology (which is scale-dependent in the case of modified gravity) only for extremely large scales, k < 0.06 h Mpc−1 at z = 0. The velocity power spectrum is substantially different in the f(R) models compared to GR, suggesting that this observable is a sensitive probe of modified gravity. We demonstrate how to extract the matter and velocity power spectra from the 2D redshift-space power spectrum, P(k, μ), and can recover the non-linear matter power spectrum to within a few per cent for k < 0.1 h Mpc−1. However, the model fails to describe the shape of the 2D power spectrum, demonstrating that an improved model is necessary in order to reconstruct the velocity power spectrum accurately. The same model can match the monopole moment to within 3 per cent for GR and 10 per cent for the f(R) cosmology at k < 0.2 h Mpc−1 at z = 1. Our results suggest that the extraction of the velocity power spectrum from future galaxy surveys is a promising method to constrain deviations from GR.