Howard suffered the injury in a collision with Posh striker Shaquile Coulthirst in Sunday's 1-0 defeat.
The 30-year-old joined Bolton in the summer from Sheffield United and had started every league game so far.
"To lose someone of his quality is a blow for us," manager Phil Parkinson told the club website.
"But it is also an opportunity for Ben Alnwick to stake his claim for a place in the team."
Bolton Wanderers goalkeeper Mark Howard could be out for 12 weeks with a broken thumb and ligament damage suffered in their League One loss at Peterborough.