Chosen by an online fan vote, Jack narrowly missed out on the top prize to Crawley Town's Enzio Boldewijn with Coventry City's Marc McNulty in second.
The on-loan Bees stopper kept three clean sheets in four league games as Keith Curle's side took seven points from a possible 12 over the course of the month. He also kept out Sheffield Wednesday when the two sides met at Brunton Park in an Emirates FA Cup Third Round tie.
In total this campaign, Jack has made 34 appearancs for The Cumbrians, keeping ten clean sheets on his season-long loan from Griffin Park.