The barnstorming number eight missed the British and Irish Lions tour due to the injury, having returned from a four-month layoff due to a knee problem in March.
Sarries director of rugby Mark McCall confirmed the England international is not scheduled to return until October, although he did not rule out Vunipola playing before then.
"He's in great condition at the moment and chomping at the bit," McCall said.
"Billy's due back some time in October, but in true Billy style he'll make it back considerably before that.
