A strained wrist cannot actually occur; strains refer to muscle injuries, while sprains refer to ligament injuries. Ligaments are the tissues that connect bones with other bones in joints, so what you may think is a strained wrist is actually a sprained wrist. The muscles in the arm near the wrist can become strained, however, though the wrist itself, which is a joint, cannot become strained. Treating what many consider to be a strained wrist is a similar process to treating sprains anywhere else in the body: the RICE treatment — Rest, Ice, Compression, and Elevation — can be used to help reduce pain and swelling and allow the injury to heal on its own.
If the wrist itself is not injured, though your initial thought was that you may have a strained wrist, the muscles that run through the arm may have been injured and will require the same treatment as that of a sprained wrist. Resting the injury means refraining from using the limb and the joint as much as possible to allow the muscles or ligaments to heal on their own. These injuries occur when the tiny fibers that make up the muscles or ligaments begin to tear, causing pain and inflammation. Allowing the affected area to rest will in turn allow the muscles or ligaments to repair themselves.
Icing the injury, whether it is a sprained wrist or what you had thought to be a strained wrist, will help reduce swelling and numb the pain associated with the injury. Icing should be done immediately after the injury and on and off for the next several hours. After a day or so, a heating pad may be applied to the injury to help alleviate pain, though this does not work for all people and can in fact make the pain worse. Try applying heat to see how your injury reacts, and if it helps, continue the practice.
Sprains generally take longer than strains to heal, so be prepared to rest the injury for a fair amount of time. Immobilizing the wrist with a brace or wrap can help prevent re-injury as well. Once the injury has healed partially or completely, it will be necessary to do some exercises to increase strength and mobility. Start with mobility exercises that help the muscles, tendons, or ligaments get used to moving the way they once did. Strength training exercises can help redevelop muscle tone and mass that may have been lost as a result of the injury, or help regain ligament strength that may have been lost.