The 24-year-old, who has scored six goals this season from ten starts, had missed the Magpies' last two games with the injury.
Best consulted the club's medical staff and it was decided he should travel to London for the operation.
Best, who has made 11 appearances in total this season, netted a hat-trick against West Ham on January 5 and also scored in the dramatic 4-4 draw with Arsenal and the 2-0 win at Birmingham.
His latest goal came in his last appearance, the 2-1 home loss to Everton on March 5.
Best had been given his chance after the sale of Andy Carroll to Liverpool and the injury will be seen as a major blow to his hopes of establishing himself in the St James' Park first team.