Medical Student Education Authorization Act of 2023 This bill provides statutory authority for the Medical Student Education Program, which provides matching grants for educating and training medical students and encouraging them to serve as primary care physicians in tribal, rural, or medically underserved communities. The Health Resources and Services Administration (HRSA) must award the grants to public institutions of higher education located in states that rank in the top quintile of states based on their projected shortage of primary care physicians. In awarding the grants, HRSA must give priority to recipients that (1) are located in states with two or more federally recognized Indian tribes, and (2) have established or plan to establish a public-private partnership to support the implementation of the grant.