Recurrent novae are repeating thermonuclear explosions in the outer layers of white dwarfs, due to the accretion of fresh material from a binary companion. The shock generated when ejected material slams into the companion star’s wind can accelerate particles. We report very-high-energy (VHE, ≳ 100  GeV ) gamma rays from the recurrent nova RS Ophiuchi, up to a month after its 2021 outburst, observed using the High Energy Stereoscopic System. The VHE emission has a similar temporal profile to lower-energy GeV emission, indicating a common origin, with a two-day delay in peak flux. These observations constrain models of time-dependent particle energization, favoring a hadronic emission scenario over the leptonic alternative. Shocks in dense winds provide favorable environments for efficient acceleration of cosmic-rays to very high energies.