We calculate the holographic entanglement entropy (HEE) of the $Z_k$ orbifold of Lin–Lunin–Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern–Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to ${\mu }_0^2$-order where ${\mu }_0$ is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in ${\mu }_0$, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with $Z_k$ orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to ${\mu }_0^4$-order for the symmetric droplet case.