A magnetic memory device in which the memory cell of MRAM is reduced in size, and a method for producing the magnetic memory device are provided. The lower wiring is formed below the word line. The connecting hole and the plug connected to it are provided. The reading wiring and the lower layer wiring are connected through this plug. Alternatively, the local wiring is provided in the connecting hole and the reading wiring and the lower layer wiring are connected. In this way it is possible to form the connecting hole close to the word line, and hence it is possible to reduce the cell size in the direction along the bit line.