The short answer: it depends on the type of wound, so you need to discuss it with your health care professional. There are waterproof dressings available.
For wounds in general, that’s the honest answer. What follows is what detailed advice looks like for one specific kind of wound, so you can see the shape of it and know what to ask about.
Closed surgical wounds are incisions held together with stitches, clips, staples, glue or tape strips. Your surgeon will let you know when it is OK to shower or bathe after surgery. It is usually fine to shower after 24 hours.
Several points are worth knowing because of the reasons behind them.
Showers are better than baths, because the wound does not soak in the water. Soaking the wound could cause it to reopen or become infected.
The dressing comes off before bathing unless you have been told otherwise. Some dressings are waterproof, and a surgeon may suggest covering the wound with a plastic bag to keep it dry.
If the surgeon says it’s OK to rinse the wound while bathing, rinse it gently. Don’t rub or scrub it. Don’t put lotions, powders, cosmetics or other skin care products on the wound. Afterward, pat the area around the wound dry with a clean towel and put on a new dressing.
Venous leg ulcers call for the same care in the other direction: keep the dressing and the skin around it dry.
None of this is advice for an open wound. A closed surgical incision and an open wound are different situations. The detail above shows what specific instructions look like; it doesn’t replace the ones you need. For an open wound, the answer is: it depends on the wound, and the person treating it should tell you.