The Prophet Muhammad (peace be upon him) did not celebrate his birthday. This is because there is no evidence in the Quran or authentic hadith (sayings and actions of the Prophet) that he ever celebrated his birthday or encouraged others to do so.
Some scholars argue that celebrating birthdays is a practice that originated outside of Islam and was not part of the culture of the Arabian Peninsula at the time of the Prophet. Others maintain that focusing on the Prophet's life and teachings should be the priority, rather than celebrating a specific date.
While there are different interpretations, the general consensus among many Muslims is that celebrating the Prophet's birthday is not considered an essential part of Islamic practice.