The solid/liquid interface migration in Nb-doped $SrTiO_3$ and its effect on dielectric properties have been investigated. The specimen sintered in air shows no migration during oxide infiltration treatment in air, whereas the specimen sintered in $5H_2-95N_2$ shows appreciable migration during similar infiltration. In the migrated layers of the specimen sintered in a reducing atmosphere, no cations of the infiltrants are detected by wavelength dispersive spectroscopy. These results show that nonstoichiometry due to the atmosphere change can induce the interface migration as in the case of frequently observed migrations due to solute concentration change. The driving force for the migration is discussed in terms of the coherency strain energy in a thin diffusional oxidized layer of the receding grain. The interface migration caused by nonstoichiometry could be suppressed by preoxidizing grain surfaces before oxide infiltration treatment. The suppression of migration increased the effective dielectric constant of the material.