What is a good moisturizer for skin while on solodyn (minocycline)?

Moisturizer. There are various good moisturizers out there. Most important is an oil-free moisturizer that says "non-comedogenic" or non-acne producing.
Non-comedogenic. Try a light non-comedogenic lotion applied to the face when it is dry from using acne products. Solodyn (minocycline) should not cause much dryness, rather the topical acne medications are usually the culprits when it comes to dry skin from acne treatment. Try aveeno ultracalming face lotion, cerave am, cetaphil lotion, or eucerin facial moisturizer.