Provided are a rolled Mg alloy material whose mechanical properties are locally different in a width direction, a Mg alloy structural member produced by plastically working the rolled Mg alloy material, and a method for producing the rolled Mg alloy material. The method for producing a rolled Mg alloy material includes rolling a Mg alloy material with a reduction roll. The reduction roll has three or more regions in the width direction. The temperature is controlled in each of the regions so that a difference between a maximum temperature and a minimum temperature exceeds 10° C. in the width direction of a surface of the reduction roll. The rolled state in the width direction is varied by varying a difference in temperature over the width direction of the reduction roll. As a result, it is possible to produce a rolled Mg alloy material whose mechanical properties are locally different in the width direction.