Bucks boss Gavin Cowan is re-shaping his squad after a run of disappointing results and Brown is the second departure of the week, while two have come in the opposite direction.
The former Crewe youngster, 23, will spend the next couple of months with the Pitmen, who play one step below Cowan's men.
He has made six appearances in the National North this term, scoring once in the 1-0 win at Southport and was part of the squad kept on from last season.
Brown follows Steph Morley – who joined Leamington on a permanent deal – out of the New Bucks Head.
Left wing-back Riccardo Calder has checked in from Bradford Park Avenue alongside free agent right-back Arlen Birch.
The Bucks are without a fixture this weekend due to their FA Cup exit and next face National North leaders York City at home on Saturday week. No further moves in or out are expected over the weekend.