Kenny Jackett's side will welcome the Posh to Fratton Park the week commencing Monday, January 21.
The Blues are enjoying their best-ever run in the much-maligned competition.
They picked up maximum points from Southern Section Group A following wins over Gillingham, Crawley and Tottenham under-21s.
Pompey defeated Arsenal under-21s in the second round, before comfortably beating Southend 2-0 on Tuesday.
Jackett's men delivered a 2-1 victory over Peterborough in League One earlier this season.Â