We present a classical treatment of the ionization and electron-capture processes in the interaction of protons with neutral noble-gas atoms, namely, Ne, Ar, Kr, and Xe. We used a three-body classical-trajectory Monte Carlo (CTMC) method to calculate the total (TCS) and differential (DCS) cross sections of single-electron processes. The Garvey-type model potential was employed in the CTMC model to describe the collision between the projectile and the target, accounting for the screening effect of the inactive electrons. The TCSs are evaluated for impact energies in the energy range between 0.2 keV and 50 MeV for a number of sub-shells of the targets. The ionization DCS are evaluated for an impact energy of 35 keV, focusing on the outer sub-shells only. We found that our ionization and electron-capture TCSs are in very good agreement with the previous theoretical and experimental data for all targets. Moreover, we presented single (SDCS)- and double (DDCS)-differential cross sections as a function of the energy and ejection angle of the ionized electron for all collision systems.