Do you want anhydrous salt, octahydrate or hexahydrate? Octahydrate and hexahydrate can be purified by recyrstallization form water (below/above 43 C), the anhydrous salt can be prepared as etherate. Z. Anorg. Chem., 1921, 119, 115; and 1948, 256, 25.

according to purification of chemicals methods you can purified magnesium iodide by Crystd from water (1.2mL/g) by partial evaporation in a desiccator.

Sublimation may be a good method.

Thx all. Peter do you know temperature and pressure conditions for the sublimation?