The 30-year-old will make his debut against the Blades' Yorkshire rivals Doncaster on Saturday.
Simonsen has been drafted in by manager Kevin Blackwell after Mark Bunn was recalled from his loan spell by Blackburn.
Blackwell told the club's official website: "Ian Bennett is our recognised number two and I decided that with the position we are in we needed a new number one.
"Steve Simonsen is a very good goalkeeper with a real presence and he was a big feature of Stoke's promotion to the Premiership. We are taking him for a month and will see what the situation is then."