Under the new system, people would be sent information if they came into contact with someone who was infected and the same information would be passed on to special regional headquarters set up to fight the respiratory disease pandemic.
The Kremlin said the measure was legal and part of a raft of measures Russia is taking to try to halt spread of the virus.
The measure will trace "citizens who are in contact with patients with new coronavirus infection on the basis of information from cellular operators about the geolocation of a cell phone of a particular person, which would allow citizens to be notified (over the phone) if they have been in contact with a person suffering from the new coronavirus, sending relevant messages to inform them of the need for self-isolation..." the communications ministry said in a statement.
Russia, which has a temporary ban on the entry of foreigners in place, has 438 confirmed cases of coronavirus so far and one virus-related death - less than many European countries.
On Monday, Moscow Mayor Sergei Sobyanin told residents of the Russian capital over the age of 65 and those with chronic illnesses to remain at home.
Russia is gradually tightening quarantine rules and readying its healthcare system for more cases. Sobyanin told the elderly and other vulnerable residents to only make trips to pharmacies and shops if absolutely necessary from Thursday until April 14.
STAY AT HOME OR DACHAS
Where possible, he also advised the elderly to leave the city and stay at their dachas - out-of-town cottages on private plots of land which many Russian families traditionally own.
The city, which has 262 confirmed infections out of the total of 438 reported across Russia, will give 4,000 roubles ($49) to all over 65s and people with chronic illnesses.
City hall has required mobile phone operators not to switch off phone and internet access for the elderly if their balance hits zero, and temporarily canceled fines for late payment of utility bills.
Moscow has also changed its coronavirus testing system. Samples will no longer be sent to a lab in Siberia for a second round of testing to confirm a positive result received during tests conducted in labs in the capital, the city's coronavirus response headquarters said in a statement.
"The diagnosis of 'coronavirus infection' will be registered after the first positive test...Repeated testing, if necessary, will also be conducted in Moscow," the head office said.
Russia is also taking steps to prepare its food supply and medical system for a potential upsurge in coronavirus cases.
The government said on Monday it had asked the agriculture ministry and other officials to prepare proposals on whether exports of any food, essential products or medicine should be limited.
The government also ordered the labor and justice ministries to devise plans to prevent workers from being fired for coronavirus-related reasons, such as self-isolation."I believe that overall, we have the situation with coronavirus under control," Mishustin said. "But preparation for more serious challenges is necessary."