Through the use of the piecewise-linearity condition of the total energy, we correct the self-interaction for the study of polarons by constructing nonempirical functionals at the semilocal level of theory. We consider two functionals, the gamma DFT and mu DFT functionals, both of which are based on the addition of a weak local potential to the semilocal Hamiltonian to enforce the piecewise-linearity condition. We show that the resulting polaron properties are in good agreement with reference hybrid functional calculations. This supports the use of semilocal functionals for calculating polaron properties.