Classical novae are cataclysmic binary star systems in which the matter of a companion star is accreted on a white dwarf (WD). Accumulation of hydrogen in a layer eventually causes a thermonuclear explosion on the surface of the WD, brightening the WD to ~10^5 solar luminosities and triggering ejection of the accumulated matter.They provide extreme conditions required to accelerate particles, electrons or protons, to high energies. Here we present the detection of gamma rays by the MAGIC telescopes from the 2021 outburst of RS Ophiuchi (RS Oph), a recurrent nova with a red giant (RG) companion, that allowed us, for the first time, to accurately characterize the emission from a nova in the 60 GeV to 250 GeV energy range. The theoretical interpretation of the combined Fermi-LAT and MAGIC data suggests that protons are accelerated to hundreds of GeV in the nova shock. Such protons should create bubbles of enhanced Cosmic Ray density, on the order of 10 pc, from the recurrent novae.