The 33-year-old has been out of action since his side's win over Northampton Saints in the Aviva Premiership on March 22.
Braid has scored seven tries in 23 matches for Sale during the current campaign.
"His leadership is second to none, he's been fantastic for the club," Sale director of rugby Steve Diamond told BBC Sport. "He puts his body on the line time and time again."
Sale host Leicester Tigers this weekend before finishing their league campaign away to London Irish on May 10.