I would not recommend microdermabrasion as an effective treatment for melasma. Melasma is a deep, resistant form of hyperpigmentation. Microdermabrasion exfoliates exfoliates the skin at a superficial level, so it would be unable to reach the damaged skin cells. To correct melasma, it is necessary to reach the dermis of the skin, where the melasma is contained.
The best approach for treating melasma is a combination of a prescription topical regimen and chemical peels. The topical regimen should include a hydroquinone product with a minimum of 4% strength, and a tretinoin product at a strength appropriate for your skin type and condition. Hydroquinone helps to suppress the overactive pigment-producing cells, and tretinoin exfoliates the skin and repairs cellular damage while helping to drive the hydroquinone deeper into the skin. There are several good skin care lines that offer products which include these ingredients in various forms, so there are options available to suit your particular needs and preferences. As for chemical peels, there are different types of acids that will help this condition. In this instance, the depth of the peel is more important than the particular peeling agent used.
As with any procedure, it is very important to work with a practitioner who is very skilled in administering the particular peel that they are providing. This becomes even more important with a more aggressive procedure. There are a few very good peels on the market right now that have been designed specifically to treat melasma, and have also been formulated to improve patient safety.