The property of superfluidity, first discovered in liquid 4 He, is closely related to the Bose--Einstein condensation (BEC) of interacting bosons 1 . However, even at zero temperature, when the whole bosonic quantum liquid would become superfluid, only a fraction of it would remain Bose--condensed at zero momentum 2 . This is due to quantum depletion phenomenon, whereby particles are excited to larger momenta states due to interparticle interactions and quantum fluctuations. Quantum depletion of weakly interacting atomic BECs in thermal equilibrium is well understood theoretically 3 but is difficult to measure 4-7 . Driven--dissipative systems, such as condensates of exciton--polaritons (photons coupled to electron--hole pairs in a semiconductor) are even more challenging, since their nonequilibrium nature is predicted to suppress quantum depletion 8 . Here, we observe quantum depletion of an optically trapped 9 high--density exciton--polariton condensate 10,11 by directly detecting the spectral branch of elementary excitations populated by this process. Analysis of the population of this branch in momentum space shows that quantum depletion of an exciton--polariton condensate can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the fraction of matter (exciton) in an exciton--polariton. Our results reveal the effects of exciton-polariton interactions beyond the mean--field description and call for a deeper understanding of the relationship between equilibrium and nonequilibrium BECs.