Quantum impurities, such as nitrogen vacancy (NV) centers in diamond, exhibit excellent quantum coherence, single-spin sensitivity, and a significant capability to be optically manipulated. These defects act as single spin sensors, allowing the detection of local magnetic fields on length scales of tens of nanometers. Their relaxation rates, affected by the magnetic noise in their vicinity, could capture information about the dynamics of a magnetic environment. In recent years, NV centers have been increasingly utilized to measure magnetic properties of ferromagnetic materials and, on a few occasions, to study antiferromagnets with uniaxial anisotropy. Both systems have the capability to propagate spin waves, whose quanta are called magnons. However, a complete theoretical description of how NV centers interact with antiferromagnetic magnons is still a topic to explore. In this work, we calculate the NV center relaxation rates considering collinear anisotropic antiferromagnetic insulators, such as MnF2 2 and NiO, represented as magnon systems. For an easy-axis of anisotropy z " and an external magnetic field H 0 , we did these calculations for both H 0 H z " (antiferromagnetic phase) and H 0 1 z " (canted phase), finding that the relaxation rates are greater in the canted phase. Moreover, we found that NiO induces remarkably lower relaxation rates than MnF2, 2 , because of its high effective exchange field mu 0 H E 1000 T.