A magnesium alloy sheet having good press formability, a magnesium alloy structural member produced by pressing the sheet, and a method for producing a magnesium alloy sheet are provided. The magnesium alloy sheet is composed of a magnesium alloy containing Al and Mn. When a region from a surface of the alloy sheet to 30% of the thickness of the alloy sheet in a thickness direction of the magnesium alloy sheet is defined as a surface region and when a 200 μm2 sub-region is arbitrarily selected from this surface region, the number precipitated impurity grains containing both Al and Mg and having a maximum diameter of 0.5 to 5 μm is 5 or less. When a 50 μm2 sub-region is arbitrarily selected from the surface region, the number of crystallized impurity grains containing both Al and Mn and having a maximum diameter of 0.1 to 1 μm is 15 or less. In the grains of the crystallized phases, the mass ratio Al/Mn of Al to Mn is 2 to 5. The magnesium alloy sheet has good press formability since the crystallized phases and precipitates that cause breaking are small in amounts contained and in size.