"Cardoso sustained the injury during training last Thursday, resulting in a severe sprain that has affected the joint," Atletico said in a statement.
It is the latest setback for Cardoso, whose debut season at Atletico has been hampered by injuries. The 24-year-old also saw limited action during the March international window, playing only 45 minutes in a friendly against Belgium.
US coach Mauricio Pochettino is expected to name his 26-man World Cup squad later this month, with the co-hosts already facing injury concerns.
Captain Christian Pulisic recently missed matches for AC Milan with a muscular problem, while Marseille winger Tim Weah and Olympique Lyonnais midfielder Tanner Tessmann have also been sidelined.
The US, who co-host the tournament alongside Mexico and Canada, will play Senegal on May 31 and Germany on June 6 in warm-up matches before opening their Group D campaign against Paraguay in Inglewood, California, on June 12.
They will also face Australia and Turkey at the finals.