As an F-1 student, do I need CPT authorization for an internship outside of the U.S.?

No, CPT work authorization is for the USA only. If you receive an offer for another country, you will need work authorization for that country, either as a local citizen or by applying through the employer. Contact International Education at educationabroad@utdallas.edu for more information prior to making any travel plans. If you leave the U.S., remember to let ISSO know.