Context. Ultra-hot Jupiters have dayside temperatures at which most molecules are expected to thermally dissociate. The dissociation of water vapour results in the production of the hydroxyl radical (OH). While OH absorption is easily observed in near-infrared spectra of M dwarfs, which have similar effective temperatures as ultra-hot Jupiters, it is often not considered when studying the atmospheres of ultra-hot Jupiters. Ground-based high-resolution spectroscopy during the primary transit is a powerful tool for detecting molecular absorption in these planets. Aims. We aim to assess the presence and detectability of OH in the atmosphere of the ultra-hot Jupiter WASP-76b. Methods. We use high-resolution spectroscopic observations of a transit of WASP-76b obtained using CARMENES. After validating the OH line list, we generate model transit spectra of WASP-76b with petitRADTRANS. The data are corrected for stellar and telluric contamination and cross-correlated with the model spectra. After combining all cross-correlation functions from the transit, a detection map is constructed. Constraints on the planet properties from the OH absorption are obtained from a Markov chain Monte Carlo analysis. Results. OH is detected in the atmosphere of WASP-76b with a peak signal-to-noise ratio of 6.1. From the retrieval we obtain Kp = 232 ± 12 km s−1 and a blueshift of − 13.2 ± 1.6 km s−1, which are offset from the expected velocities. Considering the fast spin rotation of the planet, the blueshift is best explained with the signal predominantly originating from the evening terminator and the presence of a strong dayside-to-nightside wind. The increased Kp over its expected value (196.5 km s−1) is, however, a bit puzzling. The signal is found to be broad, with a full width at half maximum of 16.8−4.0+4.6 km s−1. The retrieval results in a weak constraint on the mean temperature of 2700–3700 K at the pressure range of the OH signal. Conclusions. We show that OH is readily observable in the transit spectra of ultra-hot Jupiters. Studying this molecule can provide insights into the molecular dissociation processes in the atmospheres of such planets.