A power semiconductor module having at least one fuse. The power semiconductor module comprises a housing, load terminal elements that lead outside of the housing, and a substrate disposed inside the housing with a plurality of metal connecting tracks of different polarity electrically insulated from one another. On at least one of these connecting tracks, at least one power semiconductor component is disposed and is connected correctly in terms of circuitry to first connecting elements that have a first line cross section. The fuse comprises a second connecting element that has a second line cross section, less than the first, and is disposed between two connecting tracks and/or between a connecting track and a load terminal element. The second connecting element is sheathed in one portion by an explosion protection means.