Yes, eye infections are common in newborns.
Babies do not have a strong immune system like adults and so, they easily catch infections. Catching cold makes your baby more prone to catch an eye infection. Viral eye infections are more common in babies. Exposure to allergens like household chemicals, dust, smoke and pollen, eye injuries and blocked tear ducts can also cause pink eye in babies.
If your baby gets eye infection often, you'd better take it to see the doctor immediately. The doctor can diagnose what kind of infection the baby get and give you proper suggestions.