<p>The optimal packing of Minkowski unit spheres on a plane is analyzed. The moduli space (parameterization) of admissible lattices of doubled Minkowski spheres, which contain three pairs of points on the corresponding Minkowski sphere each and determine the packing lattices of Minkowski unit spheres, is constructed. According to the results of the proof of Minkowski’s hypothesis about the critical determinant, a partition of the Minkowski spheres into three classes is obtained: Watson spheres, Davis spheres, and Mordell–Chebyshev spheres. The lattices that optimize the packings of these spheres are indicated, and the densities of these optimal packings are found.</p>