What is the ruling on celebrating children’s birthdays?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Muslims have only two lawful celebrations; namely, ‘Eed Al-Adh-ha and ‘Eed Al-Fitr. The evidence for this is a narration on the authority of Ibn Maalik that when the Prophet, sallaallaahu ‘alayhi wa sallam, came to Al-Madeenah, the people there had two days that they used to celebrate. The Prophet, sallaallaahu ‘alayhi wa sallam, asked them about these two days. They said that they used to celebrate these two days during the pre-Islamic era. The Prophet, sallaallaahu ‘alayhi wa sallam, told them that Allaah The Exalted had replaced these two days with the ‘Eeds of Al-Adh-ha and Al-Fitr. [Abu Daawood]

This Hadeeth (narration) proves that if the Prophet, sallaallaahu ‘alayhi wa sallam, knew there were other lawful feasts, he would have told the Companions about them. Moreover, celebrating birthdays is an imitation of the disbelievers, and Muslims should be distinct in every thing. In fact, imitating disbelievers is prohibited and it may lead to them being distracted from Islam, if it is accompanied by love and  loyalty for their customs. This idea is supported by many texts.

Allaah Knows best.