Rondo suffered the injury in a fall at his home on Thursday night.
Rondo, 28, will miss training camp and preseason, but the six-week prognosis for a return should find him back in the lineup within several games of the regular season's start.
After missing parts of the past two seasons recovering from a torn ACL in his right knee, Rondo's hopes for an injury-free comeback season have already been sullied. He's entering the final season of a five-year contract and could become a free agent in the summer of 2015. Nevertheless, Boston has shown a strong desire to re-sign him to an extension, and Rondo has publicly and privately expressed a desire to continue his career in Boston.
In 30 games last season, Rondo averaged 11.7 points, 9.8 assists and 5.5 rebounds.
Rondo's injury will give first-round pick Marcus Smart a chance to play a more prominent role for the Celtics in the preseason. Smart, out of Oklahoma State, has impressed the Celtics since joining them in summer league.
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