A method of manufacturing a magnesium alloy sheet comprising by mass 7.3 % to 16% Al, 0.1% to 5 % of at least one element selected from Zn, Mn, Si, Be, Ca, Sr, Y, Cu, Ag, Sn, Li, Zr, Ce Ni, Au, and rare-earth elements except Y and Ce, and balance being Mg, having Al-rich intermetallic compounds with an average particle size of 3.0 μm or less and with a total area percentage of 11% or less, the method comprising: preparing a cast material of the magnesium alloy by a continuous casting process; performing solution heat treatment of the cast material at a holding temperature of at least a minimum holding temperature for a holding time of one hour or more to 25 hours or less to manufacture an intermediate-solution-heat-treated material, the minimum holding temperature being a temperature 10 °C lower than a temperature at which Al is dissolved in Mg in a Mg-Al binary phase diagram; and performing at least one pass of hot rolling to the intermediate-solution-heat-treated material to manufacture a rolled sheet, the hot rolling being at a temperature of 150 °C or more and 280 °C or less; wherein: after the solution heat treatment the thermal history of the material is controlled so that the total time of holding the material at a temperature of 150 °C or more and 300 °C or less is 12 hours or less and the material is not heated to a temperature of more than 300 °C; and after final hot rolling, the average cooling rate of the material from the starting temperature of cooling to a material temperature of 100 °C or less is 5 °C/min or more, the average cooling rate being determined by measuring the material temperature at the beginning of cooling after the final hot rolling and calculating the average cooling rate using (Tmp - 100)/t(°C/min), where Tmp (°C) denotes the measured temperature and t(min) denotes the time to reach 100°C. preparing a cast material of the magnesium alloy by a continuous casting process; performing solution heat treatment of the cast material at a holding temperature of at least a minimum holding temperature for a holding time of one hour or more to 25 hours or less to manufacture an intermediate-solution-heat-treated material, the minimum holding temperature being a temperature 10 °C lower than a temperature at which Al is dissolved in Mg in a Mg-Al binary phase diagram; and performing at least one pass of hot rolling to the intermediate-solution-heat-treated material to manufacture a rolled sheet, the hot rolling being at a temperature of 150 °C or more and 280 °C or less; after the solution heat treatment the thermal history of the material is controlled so that the total time of holding the material at a temperature of 150 °C or more and 300 °C or less is 12 hours or less and the material is not heated to a temperature of more than 300 °C; and after final hot rolling, the average cooling rate of the material from the starting temperature of cooling to a material temperature of 100 °C or less is 5 °C/min or more, the average cooling rate being determined by measuring the material temperature at the beginning of cooling after the final hot rolling and calculating the average cooling rate using (Tmp - 100)/t(°C/min), where Tmp (°C) denotes the measured temperature and t(min) denotes the time to reach 100°C. <EOS>