If you need to wash your harmonica comb quickly, you can rinse it under lukewarm water and then tap the comb to remove any excess water. Afterward, it would be best to place the comb out of its case for it to dry.
If you want to clean it more, you can soak it in the water and add a couple of drops of vinegar. Add mouthwash to the water while cleaning the instrument. Dry the outside of your harmonica before re-inserting it into its cover.
If you have a metal or wooden comb, do NOT run water through it. However, if you have a plastic or sealed wood comb, you can run water through it.