The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) Stellar Library (MaStar) is a large collection of high-quality empirical stellar spectra with resolution R~1800 and wavelength coverage of 3622-10354 A. In this work, we derive four physical parameters for over 68,000 spectra in the library: effective temperature (Teff), surface gravity (log g), metallicity ([M/H]), and alpha-element abundance ([α/M]). These parameters are derived using a flexible data-driven algorithm called The Cannon (Ness et al. 2015; Casey et al. 2016). We use the subset of ~3000 MaStar targets that have also been observed in other large surveys as a reference set, adopting independently derived parameters from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), the Large Sky Area Multi-Object Fibre Spectroscopic Telescope survey (LAMOST), and the Sloan Extension for Galactic Understanding and Exploration (SEGUE). The reference set is used to train The Cannon model, and subsequently applied to derive the parameters for the rest of the library. This parameter catalog, as well as results from parallel efforts, will be available as part of the 17th public data release of the Sloan Digital Sky Survey in July 2021.