It was initially feared that the 26-year-old New Zealand international, who arrived from Pro 14 side Ulster during the summer on a reported bumper £1million-a-year deal, would be sidelined for up to six months after suffering the injury during a pre-season encounter against Connacht.
However, following more examinations of the injury, head coach Pat Lam has revealed that Piutau is facing more like six weeks out of action and could be back by the end of October.
Speaking on the back of their 17-10 win against Bath in their Premiership opener, he added: "It's great that he won't be sidelined for too long.
"We don't want to lose somebody of Charles' ability for any amount of time, but that's the nature of the sport and it really underlines the importance of having depth and quality in every position.
"Charles is a hugely positive person and he's raring to go with his recovery."