The typical timetable for a return to play after a fractured tibia is eight to 10 weeks, the Angels said in announcing the injury, which was revealed in a CT scan.
La Stella had fouled a ball off his right shin in the sixth inning of Tuesday night's game at the Texas Rangers and had to be helped off the field.
In his first season with the Angels and sixth in the major leagues, La Stella is batting .300 with 49 runs scored, 16 home runs and 44 RBIs. All the totals are career highs.
The 30-year-old was named an All-Star for the first time in his career on Sunday.
Also on Wednesday, the Angels placed outfielder Brian Goodwin on the 10-day IL with a right wrist contusion.