Line an 8-inch square baking pan with foil or parchment paper.
In a heavy medium saucepan over low heat, melt the white chocolate with the butter and sweetened condensed milk, stirring constantly.
Remove from heat and add the maple extract and walnut pieces; stir until well combined.
Pour evenly into prepared pan and refrigerate at least 2 hours.
Remove from pan by lifting out the entire piece of fudge with the foil or parchment. Peel off before cutting into squares.
Store fudge in an airtight container in the refrigerator.