In Islam, there is no specific prohibition against wishing someone a happy birthday. However, the practice of celebrating birthdays is not explicitly mentioned in the Quran or Hadith (sayings and actions of Prophet Muhammad). As a result, Islamic scholars have different opinions regarding the permissibility of celebrating birthdays.
Some scholars argue that birthday celebrations are not allowed because they are not part of Islamic tradition and were not practiced by the Prophet Muhammad or his companions. They also raise concerns about the potential for imitating non-Islamic customs or engaging in unnecessary extravagance during such celebrations.
On the other hand, some scholars consider birthday wishes to be a simple expression of good will and not inherently problematic as long as they do not involve any prohibited activities or rituals.
Overall, the permissibility of wishing someone a happy birthday can be a matter of personal interpretation and cultural practices. If you're unsure or want to be cautious, you can express your well-wishes on other occasions, such as during Eid or any other time without specific religious implications.
As with many aspects of Islam, it's always best to seek guidance from knowledgeable and trusted religious scholars or leaders to understand the specific rulings and practices in your particular community or sect.