The objective of this work is to study theoretically the ground state energy of a donor atom located in a two-dimensional ultra-thin cylindrical nanostructure called nanoflakes for different geometries controlled by the three geometrical parameters, in an infinite confinement potential. The solution of our equations system is based on the 2D finite difference method. Our numerical calculations show that the ground state energy of a donor atom is more important in the small area of the nanoflakes. Moreover, beyond the critical regions, the donor energy becomes stable.