Ramani (82) is survived by his wife, two sons and two daughters.
Expressing grief over his death, Chief Minister Jayalalithaa said in a statement she was "deeply anguished to learn the death of N Ramani today due to illness."
"Ramani brought specialty and uniqueness to flute and elevated it (flute) which was once an accompaniment and he was a genius of flute music," she said.
He carved a niche for himself in flute music and got a host of recognitions like Sangeetha Kalanidhi, Padma Shri, and Padma Bhushan. His name was synonymous with Carnatic flute music and such was his fame, she said.