Payne, on loan from Gillingham, was forced off shortly before half-time against Huddersfield on Saturday with suspected ankle ligament damage, which would have kept the 21-year-old on the sidelines for the remainder of the season.
However, a scan has revealed nothing more serious than bruising and Payne has a chance of playing against the Hornets at the weekend.
"Jack is not as bad as feared," Posh boss Darren Ferguson told reporters on Tuesday.
"There is plenty of bruising and swelling, but only a small amount of ligament damage so he has a chance for the weekend.
"He won't train this week and we will leave to the last minute because he's become an influential player for us."