Dairy Nutrition Incentive Program Act of 2023 This bill directs the Department of Agriculture (USDA) to establish a dairy nutrition incentive program to develop and test methods to increase the purchase and consumption of dairy under the Supplemental Nutrition Assistance Program (SNAP). Specifically, the program must provide an incentive to SNAP benefit recipients for the purchase of naturally nutrient-rich dairy, which the bill defines to include fluid milk, yogurt, and cheese made from cow's milk. To carry out the program, USDA must enter into cooperative agreements with, or provide competitive grants to, state or local governments and nonprofit organizations for projects. The bill provides funding for the program for each fiscal year. USDA must provide for an independent evaluation of each project that measures, to the maximum extent practicable, the effect of incentives on purchases of naturally nutrient-rich dairy by SNAP recipients. Projects currently carried out by the USDA Healthy Fluid Milk Incentives (HFMI) program must be transitioned to the new dairy nutrition incentive program; the bill repeals the HFMI program one year after USDA certifies that the transition is complete.