After US and Canada, Motorola India last week started roll-out an Android 6.0 Marshmallow update for the Moto G (Gen 3) in India. The Indian Moto G3 is now receiving the Marshmallow update over-the-air (OTA). The company confirmed in a tweet.
It may take some time to reach all users. The Moto G3 users manually can check for update: Settings >> About Phone >> System Update.