Grease an 8x8-inch glass baking dish, and line with an 8x12-inch sheet of parchment paper. The ends will hang over the side of the dish.
Melt the white chocolate, sweetened condensed milk, and butter in a microwave-safe glass or ceramic bowl in 30-second intervals, stirring after each melting, for 1 to 3 minutes (depending on your microwave). Do not overheat or chocolate will scorch. Stir in the maple flavored extract until just combined, then add the walnuts. Pour chocolate mixture into the prepared baking dish; refrigerate until set, about 1 hour. Remove fudge by lifting the parchment paper, then cut into squares.