There is no such requirement as a part of medical device law/regulations in either USA or the EU.
In both jurisdictions, medical device regulatory law is separate from intellectual property law.
Intellectual property law however does require that applicable patent number(s), or another appropriate status-statement, be shown on a product so as to inform users and others of its patent status.
In medical device law, required labeling information is commonly allowed to be placed on the single piece packaging of a medical device that must be sterile at point of use and therefore is sterile barrier packaged, or is too small to carry the required information directly on the part itself. It's not clear to me that that special exception to the information-on-the-product rules extends to intellectual property law. You might want to check that point with your I.P. lawyer.