The exchange-hole dipole moment model of dispersion interactions of Becke and Johnson [J. Chem. Phys. 127 154108 (2007)] is implemented for calculations in solids using the pseudopotentials/plane-waves approach. The resulting functional retains the simplicity and efficiency of semilocal functionals while accurately treating dispersion interactions via a semiempirical asymptotic expansion. The dispersion coefficients are calculated completely ab initio using local quantities alone (density, gradient, Laplacian, and kinetic energy density). The two empirical parameters in the damping function are calculated by fit to a 65-molecule training set recalculated under periodic boundary conditions. Calculations in simple solids offer good results with minimal computational cost compared to electronic relaxation.