Timothy Ash, the head of emerging markets at Standard Bank, told CNBC via email that we wasn't sure the leak told us "anything we did not know already." Zach Witlin, an analyst at Eurasia Group, also doubted that it would lead to much pressure on the Russian leader as "part of Putin's power in Russia rests on his ability to always remain above the follies of any other official or associate."
Chris Weafer, senior partner at Macro-Advisory, told CNBC via email that it was embarrassing for Putin rather than damaging.
"The story comes at a time when the government is tackling the worst recession in the country since Putin became president in early 2000 and he has been waging a campaign against waste and excessive spending by state officials while promoting the message that 'we are all in this together'," Weafer said.
"The government has also been trying to tackle money-laundering with the so-called de-offshorization legislation which has had very little success so far."
Meanwhile, Eurasia Group President Ian Bremmer warned that the revelations could threaten the stability of some regimes like Russia.
"Vladimir Putin is directly caught up in this," he told CNBC Monday, claiming that the $2 billion could be "a tiny fraction of how much the Kremlin has actually been laundering."
Russia, in particular, could respond aggressively, Bremmer added. Given that the ICIJ was partially funded by billionaire George Soros' Open Society Foundation, the Kremlin may wish to respond, he noted.
"I feel fairly confident that the Kremlin will be going after the U.S., Soros, the CIA and this is going to make Russian policy towards the U.S. actually much more sharp and antagonistic," he said.
"That's the kind of thing authoritarian governments need to do to take forced transparency that makes them look bad at home, they have to gin up trouble with enemies abroad."