Encarnacion ranks among the major league leaders with 26 home runs and 70 runs batted in. He was selected for the American League All-Star team but won't be able to play in the game July 15 at Minnesota.
Encarnacion was injured while running out a double-play relay Saturday in Oakland.
Seattle Mariners third baseman Kyle Seager was selected to replace Encarnacion on the All-Star roster.
Seager, 26, is a first-time All-Star. He was batting .274 average with 13 home runs and 59 RBIs through Sunday.
Cleveland Indians center fielder Michael Bourn could sit out one month because of a strained left hamstring.
The team said an MRI exam confirmed a "mild to moderate" sprain and Bourn will sit out at least three weeks. Bourn has had issues with the hamstring all season. He was put on the 15-day disabled list Sunday.
Bourn had surgery on the hamstring in October after his first season with Cleveland. He began the season on the DL after having a setback in spring training.
He's batting .267 with seven stolen bases and 37 runs in 66 games.
The St. Louis Cardinals say an MRI exam on right-hander Michael Wacha's injured shoulder showed progress, but not enough for him to resume throwing.
General Manager John Mozeliak said that Wacha, the National League Championship Series most valuable player last season, will be evaluated again in two weeks. He said continued treatment along with weight training to strengthen the area around the stress fracture was in the pitcher's best interests.
Wacha has been on the 15-day disabled list since June 18. He's 5-5 with a 2.79 earned-run average.
Mozeliak said that Joe Kelly, on the DL since April 17 because of a left hamstring strain, could return to the rotation Friday at Milwaukee.
Rangers demote outfielder Michael Choice
The Texas Rangers sent struggling rookie outfielder Michael Choice to triple-A Round Rock.
Choice, who had a .177 average with eight home runs, was demoted and infielder Donnie Murphy was designated for assignment.