The in-medium pion properties, i.e. the temporal pion decay constant f_t, the pion mass m_π ^*, and the wave function renormalization in symmetric nuclear matter are calculated in an in-medium chiral perturbation theory up to the next-to-leading order of the density expansion O(k_F^4). The chiral Lagrangian for the pion-nucleon interaction is determined in vacuum, and the low-energy constants are fixed by experimental observables. We carefully define the in-medium state of the pion and find that the pion wave function renormalization plays an essential role in the in-medium pion properties. We show that the linear density correction is dominant and the next-to-leading corrections are not so large at the saturation density, while their contributions can be significant at higher densities. The main contribution of the next-to-leading order comes from the double scattering term. We also discuss whether the low-energy theorems, the Gell-Mann-Oakes-Renner relation and the Glashow-Weinberg relation, are satisfied in the nuclear medium beyond the linear density approximation. We also find that the wave function renormalization is enhanced as much as 50% at the saturation density including the next-to-leading contribution, and that the wave function renormalization can be measured in the in-medium π ^0to γ γ decay.