A catheter clamp having a generally curved body, a first end, and a second end. Once a central or midline catheter is inserted into a patient's body, the catheter is inserted into the catheter clamp and the clamp is affixed to the patient's skin with, for example, one or more stitches, glue, adhesive bandages, and/or staples. The catheter clamp allows the catheter to adopt a bent profile without risk of kinking the catheter. In addition, when the central line catheter is installed at an interior jugular location, the catheter clamp allows the free ends of the catheter to safely hang down away from the patient's hair for greater patient comfort, ease of access by medical personnel, and reduced danger of infection. The curved profile of the catheter clamp and the catheter also reduces the likelihood that the catheter will be accidentally pulled out or dislodged if the catheter is pulled on.