This is not a simple question to answer without being able to see yor baby.The important point is that the front of her tongue and her lips are nice and pink so this is not due to a heart problem. This blue colour may occur with vigorous sucking on a teat especially if she is being bottle fed. Another cause is a form of birthmark known as an hemangioma of the tongue. As this is rather unusual and your baby is still very young it would be best to ask your paediatrician to see her.
The information provided does not constitute a diagnosis of your condition. You should consult a medical practitioner or other appropriate health care professional for a physical exmanication, diagnosis and formal
advice. Health24 and the expert accept no responsibility or liability for any damage or personal harm you may suffer resulting from making use of this content.