No, it is not a sign of eye diseases. Actually, it is normal. Everyone will get dark circles under eyes because of fatigue and inadequate sleep. If babies always cry at night and do not have enough sleep, it is easy to lead to dark circles under eyes. And it is also because of melanin gathers under eyes. But melanin shouldn't be too much. Babies cannot have strong ability of metabolism, so some fresh juice can help with melanin.
It is not very often seen that new babies have got black circles under eyes. If a new baby has black circles, then it might be caused by a certain disease in the kidney or liver, lack of good sleep, or malnutrition. A recent medical research has indicated that the black circles seen on a new baby may as well be relevant with rhinitis. To avoid black circles happening on new babies, there are some measures. First of all, you should make the baby develop a regular life style, and let the baby lie and sleep on the back with a soft pillow instead of sleeping on the stomach. Secondly, add more supplements such as vitamin A, C, E. In addition, choose fine and smooth skin care cream intended for little babies only. Besides, make sure that the baby takes in adequate water everyday for metabolism. If the conditions of black circles are still serious after you have taken these measures for some time, you had better take the baby to the doctor's for an overall examination.
Well, nowadays, dark circles can be very normal for many people to have. And the common reason is lack of sleep, stress, bad habit, and some other hereditary factors. But on the other hand, it is very normal for baby to have dark circles too. First, as we know that we all have thinner skin under our eyes than on the rest of our faces. And this means blood vessels under the skin can make the area around the eyes look darker. In that way, it will just make the dark circles under his eyes more obvious. Also, tiredness can make the dark circles stand out more. This will make the blood vessels underneath his skin look darker. By the way, hereditary reasons can be possible too. So you can just check these with your baby.