We calculate Alfvén eigenmodes within a magnetic island (MiAE) which have been conjectured over a decade ago. Starting from a cylindrical plasma equilibrium, we calculate the complete metric of the island interior assuming an iota profile with a constant shear for Wendelstein 7-X parameters. Then, we solve the resulting Magneto-Hydrodynamic equations inside the island optionally considering Finite Larmor Radius corrections. We find various eigenmodes in the lowest gaps for n = 0. The eigenmode with the lowest frequency shows a weakly non-linear dependence on the island width which deviates considerably from an earlier estimate.