Preventing Antibiotic Resistance Act of 2017 This bill amends the Federal Food, Drug, and Cosmetic Act to require the Food and Drug Administration (FDA) to refuse a new animal drug application if the drug is a medically important antimicrobial used to treat humans and the applicant fails to demonstrate that the drug meets specified criteria for use in animals, including that: (1) the drug is effective, (2) the drug is targeted to animals at risk of developing a specific bacterial disease, (3) the drug has a defined duration of therapy, and (4) there is not a reasonable probability of risk to public health from microbial resistance to the drug. The FDA must review the approvals of certain medically important antimicrobials approved for use in food-producing animals. Sponsors of these drugs must submit evidence to the FDA that demonstrates that their drug meets the criteria described above for approved indications. The FDA must withdraw approval for any indication for which there is insufficient evidence that the drug meets the criteria. This bill declares that a veterinarian-client-patient relationship should ensure that medically important antimicrobials are used in food-producing animals in a manner consistent with best practices.