Line an 8×8-inch baking pan with parchment paper, leaving enough overhang on the sides to easily lift the fudge from the pan.
Add the chocolate chips, sweetened condensed milk, and butter to a medium saucepan. Cook over low heat, stirring frequently, until the chocolate is completely melted and the mixture is smooth.
Remove the saucepan from the heat. Stir in the peppermint extract.
Pour the fudge mixture into the prepared pan and spread it into an even layer.
Sprinkle the crushed candy canes evenly over the top, gently pressing them into the fudge so they stick.
Refrigerate for 2 to 3 hours, or until the fudge is completely firm.
Lift the fudge from the pan using the parchment paper. Cut into small squares and serve.