The regulation was due to come into effect on Sunday, the BBC reported.
While signing up for a new mobile or mobile data services, customers are required to show their national identification cards and get photographed.
From now on, they will also have to get their faces scanned to help verify they are genuine match to the ID provided.
Authorities have been seeking to verify the identities of hundreds of millions of Internet users in China. The Chinese government maintains that it wants to "protect the legitimate rights and interests of citizens in the cyberspace".
Facial recognition technology is already in use in China to survey the population. It is a world leader in such technologies, but more and more use of these across the country has sparked a debate.
The new regulation for telecom operators was framed by the Ministry of Industry and Information Technology as a way to "strengthen" this system and ensure that the government can identify all mobile phone users. Most Chinese Internet users access the web via their phones.
Jeffrey Ding, a researcher on Chinese Artificial Intelligence at Oxford University, was quoted by the BBC that one of China's motivations for getting rid of anonymous phone numbers and Internet accounts was to boost cybersecurity and reduce Internet fraud.
But another likely motivation, he said, was to better track the population. "It's connected to a very centralised push to try to keep tabs on everyone, or that's at least the ambition," he said.
( With inputs from IANS )