The decree amends an existing law with a new clause that says "providing communication services on data transfer and Internet connection will be done by the operator... after user identification."
The Wi-Fi connection provider would have to collect the user's full name and passport information, and would have to store the data for six months, along with details of how long the person was logged on, according to the decree.
The regulation is the latest blow to Russian Internet users, with opponents of President Vladimir Putin denouncing it as yet another attempt to control even the tiniest dissent.
"This is as bad as it sounds and even slightly worse," Russian protest leader Alexei Navalny wrote on his blog.
"Before our eyes a real "big brother" is being created... a system that knows who wrote what, where, and from what device," he said.
Contradictory explanations from various officials surfaced after the criticism, with the Moscow city government saying the measure would only effect Internet zones in Russia's post offices.
The communications ministry said the measure was a part of Russia's crackdown on terrorism, and that private Wi-Fi networks established by individuals would not be affected.
"If the Wi-Fi network is established by a communications operator, he has to ask the user to provide ID data via a text message or a special form before providing access," the ministry said in a statement.
But the operator could also get the information by "enquiring with the relevant authorities," it said, without elaborating.
Communications Minister Nikolai Nikiforov, writing on his Twitter account, said the restrictions would be in line with global practice.
"User identification (via bank card, mobile number, etc) when accessing a public Wi-Fi is a world practice," he wrote.