The 18-year-old will now stay at the Racecourse until the end of April.
Meanwhile, Danny Williams will miss Wrexham's next two matches against Macclesfield and Notts County after getting his 10th booking of the season.
But Steve Evans and Ryan Valentine are available after finishing their bans, while Chris Llewellyn's four-game suspension ends after Macclesfield.
Garrett has been a regular fixture since arriving at the Dragons, having made 10 appearances during his two-month spell since arriving at the League Two strugglers.
The Northern Ireland Under-19 midfielder has been a regular in Stoke's reserve and Academy sides this season and has made one first-team appearance for them.
BBC