Tribal Cultural Areas Protection Act This bill provides for the preservation of tribal cultural sites on public land by establishing the Tribal Cultural Areas System. Within three years of this bill's enactment, the Department of the Interior or the Department of Agriculture (USDA), as applicable, must establish criteria for recommending tribal cultural sites for designation as tribal cultural areas for inclusion in the system, using specified factors; solicit recommendations from tribes, state historic preservation officers, and tribal historic preservation officers; review designations in local land management plans to identify tribal cultural sites that meet established criteria; consider any other relevant information; consider and evaluate tribal cultural sites for designation as a tribal cultural area for inclusion in the system; and make recommendations to Congress. The bill gives Congress the sole authority to (1) designate a tribal cultural site located on public land as a tribal cultural area for inclusion in the system, and (2) remove a tribal cultural area from the system. Congress must consider the recommendations of Interior and USDA when determining whether to make such a designation. For each congressionally designated tribal cultural area, Interior or USDA must (1) establish a tribal commission to provide guidance and recommendations on the development of a management plan for the tribal cultural area, and (2) develop a comprehensive management plan. The bill allows for self-determination contracts with tribes or tribal organizations to perform administrative or management functions within a tribal cultural area.