Mental Health Workforce and Language Access Act of 2023 This bill requires the Department of Health and Human Services (HHS) to award supplemental grants to certain federally qualified health centers (FQHCs) for recruiting and retaining mental health care providers who are fluent in another language besides English. HHS must award the grants to FQHCs that are already receiving federal assistance to support outpatient primary care for low-income individuals or other underserved populations. Additionally, HHS must give preference to FQHCs where at least 10% of the patients are best served in a language other than English.