Iceland international midfielder Arnason - who has been filling in at centre-back for the injury-hit Greens - suffered a hamstring injury during the first half of Sunday's 1-0 home defeat by Nottingham Forest.
He was replaced by on-loan Manchester United central defender James Chester, 20, who made his Championship debut alongside fellow loanee Shane Lowry, making his first home start for Argyle after shrugging off an ankle injury.
Arnason is ruled out of the clash with Posh at London Road along with Reda Johnson (knee) and experienced centre-half Chris Barker (calf).
Hungary defender Krisztian Timar will vie with Chester, who spent a spell on loan at Peterborough last season, for the starting spot alongside Lowry.
