Yes. You may have access to laundry facilities (most ships have a crew laundry-free facility open 24 hours per day), or service will be offered for a nominal fee. Depending on the position and company, uniform-free laundry may be offered for staff and officers, but not to entry level crew.
Make sure to bring lots of underwear and socks as laundry facilities may get really busy and you may want to minimize the times you MUST use it, and accommodate in between your shifts.