Read Annie Carpenter's response:
I am delighted you are thinking prevention rather than cure! The carpal tunnel is a narrow passageway on the palm side of your wrist that houses the median nerve, which serves the hand and fingers. If there is pressure on or swelling around this tunnel, the nerve—as well as numerous other tendons—can be compressed, causing what's known as carpal tunnel syndrome. This syndrome can produce numbness, pain, and weakness affecting the wrist, hand, and/or fingers.
Downward-Facing Dog should not increase the risk of carpal tunnel—but if you already have the symptoms of carpal tunnel, it could make them worse. Make sure to do the pose with your weight coming toward the knuckle side of the palm, energetically pulling up the underside of the forearm from the wrist. Doing the pose properly in this way can be a powerful preventive medicine.If Down Dog is painful, you can always do a variation of the pose with your hands pressed against a wall and your torso parallel to the floor.
Generally, a well-balanced yoga practice is considered preventative and can be symptom-reducing; it provides flexibility and strength in your wrists, shoulders, neck, and upper back. A practice that involves a great deal of jumping onto your hands and/or extreme wrist flexion it may be difficult for you, especially if you are symptomatic. If you have pain or swelling, then avoid poses that are weight-bearing on the hands until your symptoms subside.
And, of course, find a good teacher to help you create a satisfying and appropriate practice that honors your needs.