We measure x-ray magnetic circular dichroism (XMCD) spectra at the Pu M_{4,5} absorption edges from a newly prepared high-quality single crystal of the heavy-fermion superconductor ^{242}PuCoGa_{5}, exhibiting a critical temperature T_{c}=18.7 K. The experiment probes the vortex phase below T_{c} and shows that an external magnetic field induces a Pu 5f magnetic moment at 2K equal to the temperature-independent moment measured in the normal phase up to 300K by a superconducting quantum interference device. This observation is in agreement with theoretical models claiming that the Pu atoms in PuCoGa_{5} have a nonmagnetic singlet ground state resulting from the hybridization of the conduction electrons with the intermediate-valence 5f electronic shell. Unexpectedly, XMCD spectra show that the orbital component of the 5f magnetic moment increases significantly between 30 and 2K; the antiparallel spin component increases as well, leaving the total moment practically constant. We suggest that this indicates a low-temperature breakdown of the complete Kondo-like screening of the local 5f moment.