If you already have a tattoo that you got before pregnancy, breastfeeding is fine (and encouraged). Remember, breastfeeding is one of the best things you can do for your baby. It provides complete nutrition for your baby, passes your antibodies to the baby to help fight and prevent infections, and is a special time of closeness for you and your baby. There are very few reasons why a mother cannot breastfeed her baby, and having a tattoo is not one of them.
On the other hand, if you are considering getting a tattoo now, while you are breastfeeding or pregnant, think carefully about it. There are risks involved in getting the tattoo, which is made by injecting colored ink into the top layer of skin with a small needle. You could get an infection or have an allergic reaction to the ink. These generally are only minor reactions, just at the site of the tattoo, so they may or may not affect the baby. Because the ink goes into the outer layer of the skin, it should not get into the blood stream. Even if a small amount does, the ink particles probably are too large to pass into breast milk.
However, if you are breastfeeding or pregnant and you have a more severe reaction that affects your entire body, the baby would most likely be in harm's way. There also is the very small risk of getting an infection in your bloodstream (for example, hepatitis or human immunodeficiency virus) from the tattoo needle used, which would then be passed to the baby if you are breastfeeding or pregnant.
Therefore, it is best to wait until you are no longer breastfeeding or pregnant before getting a tattoo. If you decide not to wait to get a tattoo, make sure that you go to a reputable place. Ask for a recommendation from your local health department.