If you have had an injury or an operation, you should ask your physician for advice.
Other wise you should try to keep the weight on the inner edges of the hands and push the index finger mounds and all the fingertips firmly into the floor. Imagine that the energy of the hands flows through the fingertips to the mat making the balls of the hand lighter. Very important is to engage the muscles of the arms by pulling the hands energetically toward each other and lifting the upper arms away from the floor. So, you don’t “hang” in the Down Dog. It’s hard work in the beginning, because people tend to have very weak wrists nowadays due to lack of working with the hands and arms.
Also, how strong is the pain? If you are an office worker your wrists are probably very weak and it takes some time and patience to strengthen them. This is also often painful in the beginning, because muscles which usually don’t do anything have to suddenly work. The body is a bit confused and reacts with the sense of pain. You should just continue, if it’s nothing anatomical, but at the same time carefully listen to the body and learn to notice what kind of feeling it is in the wrists, is it too much, should you take a break and so on.
If the pose gets too much you should just practice all fours instead of Down Dog.
Thank you for practicing yoga with Gotta Joga!