The 24-year-old former Denmark Under-20 international has made seven appearances since joining the Potters from FC Midtjylland in 2015.
This season he has been behind Lee Grant and Shay Given in the Potters' pecking order and only played twice in the EFL Trophy.
Haugaard will provide extra cover following Adam Bogdan's knee injury.
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Wigan Athletic have signed Stoke City goalkeeper Jakob Haugaard on loan for the rest of the season.