Line an 8×8-inch baking pan with parchment paper, leaving an overhang on the sides. Lightly butter the pan to help hold the parchment in place.
Add the sweetened condensed milk, semi-sweet chocolate chips, butter, and salt to a large microwave-safe bowl.
Microwave the mixture in 30-second intervals, stirring well after each interval.
Continue heating and stirring until the chocolate is mostly melted and smooth, about 2 minutes total. The remaining chocolate should melt from the residual heat.
Stir in the vanilla extract until the fudge mixture is smooth and glossy.
Immediately pour the mixture into the prepared pan and spread it evenly with an offset spatula.
Refrigerate for at least 4 hours, or preferably overnight, until completely set.
Lift the fudge from the pan using the parchment overhang and cut it into squares with a sharp knife or bench scraper