The 31-year-old was forced off the pitch after a tackle by Middelsbrough's Jonathan Greening just 20 minutes into the draw at The Riverside at the weekend.
Trotters boss Sam Allardyce has confirmed that the Danish international has suffered damaged ankle ligaments
"Per will be out for four to six weeks with damaged ankle ligaments," Allardyce told the club's official website. "It's a blow to our plans because Per has been brilliant for us this season."
Frandsen also admitted that the injury was serious.
"I twisted my ankle badly after a challenge from behind and have ruptured the ligaments," said Frandsen.
