The team announced that the procedure was performed Wednesday by Drs. Brian McKeon and Drew Terrono at New England Baptist Hospital.
No timetable has been set for his return, but the Boston Globe reported that, according to an unnamed source, Daniels is expected to miss about eight weeks.
Via his Twitter account on Wednesday afternoon, Daniels said the surgery went well and he would "be back better than before".
The team said Daniels first noticed a problem about two weeks ago, then aggravated the injury in practice on Sunday.
The 6-foot-6 Daniels signed with the Celtics this summer after three years with the Indiana Pacers. He is averaging 5.7 points, 2 rebounds and 2.1 assists in 19 games this season.
Material from the Associated Press was used in this report.