A catheter assembly (10) is disclosed, which includes a catheter adapter (14). A port (50) is disposed in the catheter adapter to provide selective access to the interior of the catheter adapter, and can be used for fluid flushing or infusion. A valve (70) is disposed within the catheter adapter that includes a one-way valve portion (76) that prevents proximally-directed fluid flow. The valve further including a flexible tube portion (78) that covers an opening between the port and the catheter adapter.