Fostering Innovation in Medical Imaging Act of 2017 This bill amends the Federal Food, Drug, and Cosmetic Act to allow the Food and Drug Administration (FDA) to approve a medical imaging device intended to be used with an approved contrast agent when—under specified conditions—the use differs from the approved use of the contrast agent. (Contrast agents are substances used to enhance the visibility of body structures in medical imaging.) The FDA center that reviews medical devices has primary jurisdiction over such reviews. After authorization of a medical imaging device that makes new use of a contrast agent, the sponsor of the approved contrast agent may submit a supplemental application for the new use of the contrast agent.