Jio, BSNL and Vodafone are among those to have adopted the move after a request from the government.
The message, in English, begins with a person coughing and is heard instead of a ringing tone by the caller.
However, several websites have published a way to silence it, after complaints it was becoming annoying.
It contains information about the virus and its symptoms, and is heard only by the caller - it is not a default handset ringtone.