The Shakers are struggling in League Two, just one place and one point above the bottom two, and manager Chris Casper believes Schmeichel will be a useful addition.
"He's done very well for Darlington earlier this season, he's young and enthusiastic," he told Bury's official website.
"The move here will give him the chance to get some more games under his belt and with coming from such a big club can only be good for us."
Casper was forced to look for a new keeper after Craig Dootson was ruled out for the season after breaking his arm in the 0-0 draw with Barnet on Sat.
First-choice keeper Neil Edwards, formerly of Stockport and Rochdale, was already out with a shoulder injury.