The low-magnetic-field feature in the magnetic field dependence of the luminescence of negatively charged nitrogen-vacancy (NV−) centers in diamond has been experimentally observed for the first time. This feature, centered at the zero magnetic field-henceforth the zero field line-and observed with a magnetic field sweep of NV− center luminescence (magnetic spectrum), is quite narrow. The properties of this line are considerably different from those of other narrow NV− magnetic spectrum lines. Its amplitude is weakly dependent on the orientation of the single-crystal sample with respect to the external magnetic field. This line is also observed in a powdered sample. The shape of the line changes drastically with a change in the polarization of excitation light. The amplitude of the line non-linearly depends on excitation light intensity. For low intensities this dependence is close to the square law. We attribute the occurrence of this line to the dipole-dipole interaction between different NV− centers.