The Maunakea Spectroscopic Explorer (MSE) is a planned 11.25-m aperture facility with a 1.5 square degree field of view that will be fully dedicated to multi-object spectroscopy. A rebirth of the 3.6m Canada-France-Hawaii Telescope on Maunakea, MSE will use 4332 fibers operating at three different resolving powers (R ~ 2500, 6000, 40000) across a wavelength range of 0.36-1.8mum, with dynamical fiber positioning that allows fibers to match the exposure times of individual objects. MSE will enable spectroscopic surveys with unprecedented scale and sensitivity by collecting millions of spectra per year down to limiting magnitudes of g ~ 20-24 mag, with a nominal velocity precision of ~100 m/s in high-resolution mode. This white paper describes science cases for stellar astrophysics and exoplanet science using MSE, including the discovery and atmospheric characterization of exoplanets and substellar objects, stellar physics with star clusters, asteroseismology of solar-like oscillators and opacity-driven pulsators, studies of stellar rotation, activity, and multiplicity, as well as the chemical characterization of AGB and extremely metal-poor stars.