Assuming the dishwasher is a built-in, you need a cabinet around it or next to it. In lieu of a cabinet an end panel (3/4" finished plywood) could be secured to terminate the run and enclose the dishwasher. A counter would be installed on top of the cabinet frame. You would have a seam where the counter meets the old one or need to replace the entire countertop.
Hard to elaborate on this without knowing more details on your setup.