The authority could take action just after Battlegrounds Mobile India released. One of the high official of Government authority wrote a letter direct to the Indian Prime Minister to ban the game. According to him, the game is a treat to privacy and security of Indian users. However, the server of the game is in India. He also thinks the publisher of the game Krafton will share the game's data with Tencent company as they both work together in PUBG Mobile.
For more information check this: https://holotin.com/battlegrounds-mobile-india-ban-in-india-along-with-pubg-what-is-going-on/