The British & Irish Lions back-rower suffered the injury on his debut in the Aviva Premiership for Bath at the start of September, but was hoping to make a relatively swift recovery in time for the upcoming internationals.
Interim head coach Rob Howley won't be able to select the key figure in the pack for the earlier of the Tests against Australia, Argentina, Japan and South Africa in November.
However Howley feels there is hope he might be able to feature against the Brave Blossoms or the Springboks and feels his experience around the squad will be valuable in the meantime.
He said: "Taulupe is still in his rehab process and has been working closely with Bath.
"We hope he will be available in the later part of the campaign, but his experience will be vitally important to have around the squad."