The Robins are currently in a goalkeeping crisis with only Stephen Phillips currently the only fit shot-stopper at Ashton Gate.
Billy Mercer is currently at Lilleshaw for treatment on a persistent groin problem, whilst Mike Stowell (pictured) is out recovering from shoulder surgery.
The loan deal gives The Potters the option of recalling the 19-year-old within 24 hours notice, should Stoke urgently require his services.
Foster is likely to go straight into the team and on the bench for The Robins trip to resurgent Boston United on Wednesday night.
"We understand he will be playing for their reserves and also be on their first-team bench," said Stoke's Director of Football John Rudge to the club's official site.
"He is still a highly-promising young goalkeeper and the experience of going out on loan will benefit him."
