Can We Wish Islamic New Year?

Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) was asked: What is the ruling on congratulating people on the occasion of the Hijri new year, and how should one reply to a person who offers congratulations?

He replied: 

“If someone offers you congratulations, then respond to him, but do not initiate such greetings. This is the correct view concerning this matter. So if a person says to you, for example, “Happy New Year”, then you can say, “May Allah make it a good and blessed year for you.” But you should not initiate such a greeting, because I do not know of any report that the salaf [early generations of Islam] congratulated one another on the occasion of the new year, rather the salaf did not regard the first of al-Muharram as the first day of the new year until the caliphate of ‘Umar ibn al-Khattab (may Allah be pleased with him.” 

Shaykh ‘Abd al-Karim al-Khudayr said concerning offering congratulations on the occasion of the hijri new year:

“Praying for another Muslim in general terms, in phrases that are not meant as a kind of ritual  on special occasions such as ‘Eid, is acceptable, especially if what is meant by this greeting is friendship and to show a friendly face to one’s fellow Muslim. Imam Ahmad (may Allah have mercy on him) said: “I do not initiate the greeting but if someone greets me I return the greeting, because responding to the greeting is obligatory. But being the first to offer congratulations is neither Sunnah nor forbidden.”

For more on Hijrah, please see these answers: 7191 , 10063 . 

For more about celebrating Gregorian New Year, please see this answer: 177460

And Allah knows best.