The 25-year-old utility man, who joined the Pilgrims after being released by Chesterfield, sustained the injury having played just 85 minutes of pre-season football.
Manager Carl Fletcher had raised concerns immediately after his team's 1-0 victory at Truro and he told the club's official website the injury is as bad as he first feared.
"It is one of those freak injuries you get in football. It is disappointing," said Fletcher.
"We are looking at about three months, I think."
Fletcher added: "He's settled in lovely. He's a good player, a good lad, and I am really disappointed for him."