You should probably avoid swimming, going into a hot tub or participating in any activities where your tattooed skin can become soaked until it completely heals.This takes 1.5 to 3 months. At the very bare minimum, wait at least a couple of weeks. This is not only to protect or skin as it heals, but also to avoid changes or damage to your tattoo. Chlorine may alter the color of the ink as your skin is healing.
I would wait at least a week before going into the hot tub or the pool .At that time I would put a thin layer of Vaseline on the wound to protect it from any chlorine entering the area. Better safe than sorry.