Native Health and Wellness Act of 2021 This bill establishes two grant programs to improve public health services in tribal communities. First, the bill requires the Centers for Disease Control and Prevention to award grants to Indian tribes or tribal organizations for promoting health, preventing disease, and reducing health disparities among American Indians and Alaska Natives. In addition, the Department of Health and Human Services must make grants to Indian tribes and tribal organizations for recruiting and mentoring American Indian and Alaska Native youth and young adults in health professions.