1590s in the surgical sense, from compress (v.).
compress com·press (kŏm'prěs')
A soft pad of gauze or other material applied with pressure to a part of the body to control hemorrhage or to supply heat, cold, moisture, or medication to alleviate pain or reduce infection. v. com·pressed, com·press·ing, com·press·es (kəm-prěs')
To press or squeeze together.