The invention offers (a) a method of producing a magnesium-alloy material, the method being capable of obtaining a magnesium-alloy material having high strength, (b) a magnesium-alloy material having excellent strength, and (c) a magnesium-alloy wire having high strength. A molten magnesium alloy is supplied to a continuous casting apparatus provided with a movable casting mold to produce a cast material. The cast material is supplied to between at least one pair of rolls to perform an area-reducing operation (a rolling operation). The rolling operation is performed such that pressure is applied to the cast material using the rolls from at least three directions in the cross section of the cast material. A magnesium-alloy material obtained through the above-described production method has a fine crystal structure and is excellent in plastic processability.