Rowe had an operation on Wednesday and the procedure is thought to have gone well.
The 25-year-old has been hampered by a niggling knee injury for several weeks and has struggled for form this season.
It is thought he will be out of action for around six weeks.
Meanwhile, Posh have extended Hogan Ephraim's loan from QPR until January 23. The midfielder's initial one-month stay at London Road was due to expire next week.