Siegrist, a Switzerland Under-21 international, will now stay with the Brewers until February 2 from Premier League side Aston Villa.
Siegrist is yet to feature for the club - with Dean Lyness the preferred choice - but Cansdell-Sherriff has played a pivotal part in the defence, which has kept nine clean sheets during his time at the club and has propelled the team into third place.
Manager Gary Rowett told the club's official website: "Benji has massive potential and it is only because of Dean's form and the team's results that he hasn't got his chance yet. I think he has really enjoyed working with Kevin Poole and it has been great for his development.
"He is there waiting for his chance should it come his way and he will be able to show us all what we know he can do. At the moment he is keeping Dean on his toes and that's why we've extended it for another month."