Reference: al-Bid’u wal-Muhdathaat wa maa laa Asla lahu – Page 224
Fataawa fadheelatush-Shaykh Muhammad as-Saalih al-‘Uthaymeen – Volume 2, Page 302
Question: What is the ruling regarding celebrating children’s birthdays or marriage anniversaries?
Response: There are no [legislated] celebrations in Islaam except the day of Jumu’ah which is the ‘Eed of the week, and the first day of Shawwaal is the day of ‘Eed al-Fitr and the tenth day of Dhul-Hijjah is the day of ‘Eed al-Adhaa. And often the day of ‘Arafah is called ‘Eed for the people of ‘Arafah (the ones performing Hajj) and the days of Tashreeq (11th, 12th and 13th of Dhul-Hijjah) are also the days of ‘Eed following on from ‘Eed al-Adhaa.
As for birthdays of people or children or marriage anniversaries and the like, then all of these have not been legislated and are an innovation.