The 23-year-old picked up the injury during England squad training in June and was subsequently ruled out of the squad for the World Cup, to be replaced by Chelsea's Trevoh Chalobah.
"Newcastle United can confirm that Tino Livramento has successfully undergone a minor surgical procedure," the club said in a statement.
"The defender ... is expected to return during pre-season."
Livramento made only 17 Premier League appearances for Newcastle, suffering two knee injuries that ruled him out for two months before a hamstring injury in January sidelined him for 15 matches.
Newcastle begin their 2026-27 Premier League campaign against Liverpool on August 23.