The paper considers a nanowires 2D array located in the nodes of a square lattice. Computer simulations use the Heisenberg model and Metropolis algorithm. The array consists of small nanowires that are monodomain. The exchange interaction orders the spins within a single nanowire. Dipole–dipole forces act between neighboring nanowires. The shape of an individual nanowire affects its magnetic anisotropy. Computer simulations examine the phase transition temperature and magnetization behavior of the system. The type of magnetic moments ordering in the array of nanowires depends on the orientation of their long axis. We consider two types of systems. The nanowires’ long axes are oriented perpendicular to the plane of their location in the first case. A dipole–dipole interaction results in first-type superantiferromagnetic ordering of the nanowires’ magnetic moments for such orientation. The nanowires’ long axes are oriented in the plane of the system in the second case. Dipole–dipole interaction results in second-type superantiferromagnetic ordering in such systems. The dependence of the phase transition temperature on the dipole–dipole interaction intensity is investigated.