Russia's communications regulator Roskomnadzor said LinkedIn would be unavailable in the country within 24 hours.
Some internet providers have already cut access to the site, which has more than six million members in Russia.
LinkedIn told the BBC it hoped to meet Roskomnadzor to discuss the block.
In 2014, Russia introduced legislation requiring social networks to store the personal data of Russian citizens on Russian web servers.
It is the first time the law has been enforced against a US-based social network.
Analysis by Sarah Rainsford, BBC correspondent in Moscow
The Kremlin says there's nothing to worry about, but Russian social network users fear that blocking LinkedIn is only a first step.
Many believe this ban is about censorship and control, not data protection. They're concerned that more popular sites such as Facebook and Twitter will be next.
One vivid cartoon shows the grim reaper, bearing the logo of Russia's communications regulator, heading for a door with the Facebook logo. Behind him lies a trail of blood from attacks on other sites.
Another user declares that the ban on LinkedIn marks "a new era in mass censorship," while another fears that further restrictions will be creeping: "They're like sadists, doing it bit by bit."
Social media has played a critical role in organising opposition protests in Russia. Such sites have also become an increasingly important alternative source of information, as state control over traditional media has increased.
Kremlin spokesman Dmitry Peskov told journalists in Moscow that Roskomnadzor was acting strictly in accordance with Russian law.
He added that the Kremlin had no intention of intervening in the situation.
A LinkedIn spokesman said: "Roskomnadzor's action to block LinkedIn denies access to the millions of members we have in Russia and the companies that use LinkedIn to grow their businesses.
"We remain interested in a meeting with Roskomnadzor to discuss their data localisation request."
Roskomnadzor spokesman Vadim Ampelonsky told the Interfax news agency that the regulator was working out the logistics of the meeting.
Social network LinkedIn will be blocked in Russia, after a court found the company guilty of violating local data storage laws.