Those personnel are Commissioned Officers of the U.S. Public Health Service Commissioned Corps (PHSCC). The PHSCC is under the United States Department of Health and Human Services, of which the FDA is a division. The PHSCC is one of the seven uniformed services in the United States.
Though their uniforms and ranks are similar to Navy dress and working uniforms, they are not, nor do they belong to, the U.S. Navy.