Zuckerberg was to meet Prime Minister Dmitry Medvedev along with the main government pointmen on innovation in Russia, Deputy Prime Ministers Arkady Dvorkovich and Vladislav Surkov.
The government has said they will discuss cooperation in IT technology and start-ups in Skolkovo the technology hub outside Moscow that has been championed by Medvedev as a Russian equivalent of Silicon Valley.
Zuckerberg, 28, wasted no time in exploring the Russian capital after his arrival, posing for photographs in Red Square like an ordinary American tourist in one of his trademark hooded tops, Russian press reports said.
Staying true to his roots, he then headed for a meal at a nearby branch of McDonalds.
Regularly brandishing an iPad at government meetings and publishing comments on Twitter, former president Medvedev likes to promote himself as the main proponent of a drive to give Russia a more innovation-based economy.
Critics have regularly ridiculed his often banal utterances on Twitter and noted that making Russia a true innovation-based economy is still just a pipe dream.
Zuckerberg will be hoping his visit boosts Facebook's presence in Russia, one of the few major countries worldwide where it is not the number one social network.
Facebook lags well behind Russia's most popular social network VKontakte, founded by Saint Petersburg native Pavel Durov, 27, often described as the "Russian Zuckerberg."
VKontakte is aimed firmly at Russian speakers, allowing it to better respond to a very specific local market.
Zuckerberg's visit is not entirely free of controversy, with Russian firms saying his main aim is to headhunt Russian tech talent and lure recruits back to California.
While this is his legitimate right, the government should do more to keep homegrown talent in the country, the Vedomosti business daily quoted as saying the chief executive of the country's biggest IT holding IBS Group, Anatoly Karachinsky.
"If the authorities are interested in helping Russian companies then they should encourage Western firms to make their orders here just like India and China have done," he said.
Representatives of Vkontakte and Russia's largest Internet company Mail.ru confirmed to Vedomosti that Facebook had made attempts to tempt their employees out of Russia.
High standards of education in Russia and strong traditions in research make Russian programmers highly sought-after worldwide, even if now the differences in pay are not so stark between Russia and the West as they were in the 1990s.
Meanwhile, Russian also has its own homegrown Internet industry with Russian-language firms like VKontakte and Mail.ru having tens of millions of users and start-ups enjoying success in both Moscow and Siberia.
Although it is believed to be his first visit to Russia, Zuckerberg's company already has close links to the Russian Internet sector.
Russian technology investment firm DST Global, whose main shareholder is oligarch Alisher Usmanov, has a stake of at least five percent in Facebook although some observers estimate that the holding is even higher.
The anti-Kremlin demonstrations that rocked Russia since December have largely been coordinated through social networks and analysts say that the increase in Internet use poses a significant challenge for the domination of President Vladimir Putin.