Will just washing with water leach the dye from my hair?

I literally just dyed my hair this morning, and now I need to take a shower. Problem is, I can’t get out of it. Long story, but in short my hair is now impure, not greasy and curable with dry shampoo.
I however, do have the option of showering with just water. If I wash my hair with just cold water and no shampoo, will I lose a lot of color?