The effect of magnetic field on the static and dynamic spin correlations in the noncentrosymmetric heavy-fermion superconductor CePt₃Si was investigated by neutron scattering. The application of a magnetic field B increases the antiferromagnetic (AFM) peak intensity. This increase depends strongly on the field direction: for B||[0 0 1] the intensity increases by a factor of 4.6 at a field of 6.6 T, which corresponds to more than a doubling of the AFM moment, while the moment increases by only 10% for B||[1 0 0] at 5 T. This is in strong contrast to the inelastic response near the antiferromagnetic ordering vector, where no marked field variations are observed for B||[0 0 1] up to 3.8 T. The results reveal that the AFM state in CePt₃Si, which coexists with superconductivity, is distinctly different from other unconventional superconductors.