Medical Innovation Prize Fund Act This bill denies any person the exclusive right to manufacture, distribute, sell, or use a drug, a biological product, or a medication manufacturing process. The bill establishes the Fund for Medical Innovation Prizes to provide for prize payments in lieu of market exclusivity. The Board of Trustees of the fund must award prize payments to: (1) the first person to receive approval for a medication; (2) the holder of the patent for a manufacturing process; and (3) persons or communities that contributed to the development of a rewarded medication or process through the open, nondiscriminatory, and royalty-free sharing of knowledge, data, materials, and technology. The board must establish: (1) criteria for selecting recipients and determining the amount of prizes, and (2) independent expert advisory committees to assist it in carrying out this bill. The board must establish, and may periodically modify, minimum levels of funding for priority research and development, including research and development regarding global neglected diseases, orphan diseases, global infectious diseases, and other global public health priorities. The board may authorize nonprofit intermediaries to reward projects for interim research and development of products or for open source dividend prizes. The Government Accountability Office must determine the board's effectiveness in bringing to market new medications and manufacturing processes in a cost-effective manner and in addressing society's medical needs. The bill establishes an annual fee on health insurers to fund this bill.