The ink itself can't travel through the milk--or through the bloodstream if you are pregnant!--so that part of it is safe. The real concern is 1) the risk of hepatitis, which is negligible if you use a reputable place that uses new, sealed ink for each tattoo and sterilizes all equipment or uses disposable needles and 2) the risk of infection, which is mainly in the case of the person not taking proper care of the new tat.
The hardest part of getting the tattoo will be finding a tattoo artist who will agree to tattoo a mom who is still breastfeeding, because of the risks above. They don't want to be held liable if the mother gets an infection and the baby gets sick as well. If you take proper precautions and proper care, however, the risk is very low.
at 12:25 AM on Jul. 2, 2010