The England international has not played since the penalty shoot-out defeat to Real Madrid in the final of the Supercopa de Espana on January 12 due to a troublesome groin problem.
As the discomfort was not subsiding, Atleti decided to send the 29-year-old for an operation, which the club say was completed successfully.
Trippier will now begin a recovery process but is not likely to be fully fit for another month, according to reports in Spain.
It means the former Tottenham man is likely to miss the visit of Liverpool on February 18, as well as league games against Granada, Valencia, Villarreal and Espanyol.
Trippier has made 22 appearances in all competitions since moving to the Wanda Metropolitano last July for a reported fee of €22million.
Atletico are winless in their past five matches in all competitions and sit sixth in LaLiga, 13 points adrift of leaders Madrid.