There are provided a method for producing a magnesium alloy sheet having good press formability and a magnesium alloy coil stock obtained by coiling the magnesium alloy sheet. After a raw material sheet 1 composed of a magnesium alloy is preheated to 280° C. or less, the heated raw material sheet 1 is rolled with a reduction roll 3 and the obtained long rolled sheet is coiled. The surface temperature of the reduction roll 3 is set to be 230° C. or more and 290° C. or less. The preheating, rolling, and coiling are repeatedly performed in a continuous manner. By setting both the temperatures of the raw material sheet 1 and reduction roll 3 to be certain temperatures, the rolling property of the raw material sheet can be improved and the raw material sheet can be properly rolled in a continuous manner. In addition, a variation in temperature in the width direction of the reduction roll can be suppressed and uniform rolling can be performed, resulting in the production of a long magnesium alloy sheet. In this magnesium alloy sheet, working strain is sufficiently introduced by rolling and an increase in the size of crystal grains is suppressed. Thus, the magnesium alloy sheet has good press formability. Furthermore, a coil stock in which telescoping is not easily caused and that has good appearance is obtained.