Ab initio free energy perturbation calculations of solvation free energies are performed using the recently developed frozen density functional method. This method treats the solute-solvent system as a supermolecule in the density functional formulation but freezes the the electron density of the solvent molecules, while considering its effect on the solute Hamiltonian. The quality of the intermolecular interactions obtained by this method is examined by calculating the potential surface for a water dimer composed of one solute and one solvent molecule. The resulting potential surface provides a good approximation for the actual intermolecular potential of the water dimer. The same approach is then used in evaluating the solvation free energy of a water molecule relative to the corresponding solvation free energy of a methane molecule. These ab initio solvation free energies are calculated by using a classical force field as a reference for the corresponding quantum mechanical energy surface. The results of the calculations are encouraging, indicating that the frozen density functional method can be applied to studies of chemical reactions in solutions. Furthermore, the use of a classical force field as a reference state should provide a general way for performing free energy perturbation calculations by any ab initio method.