Analytical solutions of the N-dimensional non-relativistic wave equation with the non-central generalized Kratzer potential with arbitrary angular momentum have been investigated within the framework of the asymptotic iteration method. In hyperspherical coordinates, the normalized wave functions for rovibrational states are obtained in terms of generalized Laguerre and Gegenbauer polynomials. We have also derived the recurrence formulas and the radial expectation values of the reduced internuclear distances in N-dimensions. Rovibrational expectation values < nl vertical bar(r/r(e))(s)vertical bar nl >. are given for -3 <= s <= 3.