Petrucci has started both of Posh's Championship fixtures since joining the club on an initial month-long deal on January 9.
The 21-year-old midfielder told the club's official website: "I am very happy. I only signed for a month in the first place because it was my first loan spell.
"I didn't know what to expect. However, since the first few days I realised that I wanted to stay for longer and I am very pleased to be here until the end of the season."