Terahertz (THz) magnetoresistance effects have been extensively investigated and have shown promising results for applications in magnetic modulations of the amplitude of THz waves. However, THz magnetocapacitance in dielectric systems, which is essential for phase modulations of THz radiation, remains largely unexplored. Here, we study the THz response of a bulk single crystal of La_0.875Sr_0.125MnO₃ at around its Curie temperature, observing significant magnetic-field-induced changes in the THz resistance and capacitance extracted from the optical conductivity. We discuss possible mechanisms for the observed coexistence of colossal THz magnetoresistance and magnetocapacitance in a perovskite manganite that is not multiferroic. This work enhances our understanding of colossal magnetoresistance in a complex system with THz spectroscopy and demonstrates potential use of perovskite manganites in THz technology.