Brown joins fellow player Nick Farquharson on loan at the Weaver Stadium as the Dabbers look to bolster there squad as they push for promotion out of the Unibond League One (South) Division.
The left sided midfielder who can also play as a striker will be available for selection for Monday's home game against Warrington Town.
The loan signing shows the strong releationship between both clubs with Crewe already paying Nantwich Town for the services of Kelvin Mellor and Matt Freeman earlier on in the season.