The injury is expected to keep the 19-year-old out for at least two months and, with Tyrone Barnett and Emile Sinclair on the transfer list and currently out on loan at Ipswich and Barnsley respectively, Posh boss Darren Ferguson will look to sign a replacement striker in January.
He told the club's official website: "It is a massive blow because Saido has made a real impact, but he is going to be out for at least eight weeks so has returned to West Brom.
"We will look at maybe bringing him back again when he is fit, but will have to remain patient on that one.
"We will be looking to strengthen in that particular area of the field in the new year."
Berahino joined Peterborough in October and scored two goals in 10 npower Championship appearances.