Yes, I would. If it were me I would wash it in cold water with detergent and no fabric softer. If you think you have the time I would probably air dry it. If not I would partially dry it on low and then air dry the rest of the way. This should minimize shrinkage.
I have had tote bags that I have washed and dried that have shrunk so much that they looked like they were for the kids dolls!
Mary