The 21-year-old, who has yet to play for Spurs' first team, has made 18 appearances for Posh since joining the club at the end of August.
McGee was due to return to White Hart Lane at the beginning of January.
"He has been top drawer since he joined the club and he is only going to get better," Posh boss Grant McCann said.
Tottenham Hotspur goalkeeper Luke McGee has extended his loan deal at League One Peterborough United until the end of the season.