The temperature and magnetic field dependence of the magnetic structure in the singlet crystal-field ground-state system PrNi2Si2 have been determined using single-crystal neutron diffraction. At the magnetic ordering temperature in zero field, TN=20.0±0.5K , an amplitude-modulated magnetic structure sets in with a propagation vector k=(0,0,0.87) and the magnetic moments of the Pr3+ ions parallel to the c axis of the body-centered tetragonal structure. The magnetic structure remains amplitude modulated down to low temperatures (T=1.6K) with only a small tendency to squaring up, as signaled by the weak intensity of the third harmonic that develops below 16 K. With applied field along the easy axis, the modulated structure goes smoothly over into a ferromagnetic state. At the critical field of Hc=58kOe , the first harmonic disappears and the field-induced ferromagnetic moment shows a kink, in agreement with magnetization measurements. Both the temperature and magnetic field dependence are well described by a periodic field Hamiltonian including magnetic exchange and the crystalline electric field.