Eleven million documents held by the Panama-based company Mossack Fonseca were leaked to German newspaper Sueddeutsche Zeitung, then shared with the International Consortium of Investigative Journalists (ICIJ).
In Russia, the three main pro-Kremlin TV channels have not reported the story so far.
This is quite typical behaviour for Russia's mainstream broadcasters, which often steer clear of controversial topics involving Russian leaders.
The leak reveals a suspected money-laundering ring run by a Russian bank and involving close associates of President Vladimir Putin.
Kremlin spokesman Dmitry Peskov rejected the allegations: "Even though Vladimir Putin is not explicitly mentioned anywhere, it is obvious for us that our president has been and will be the main target."
The story is covered by privately owned business channel RBK and independent digital news channel Dozhd TV - sources that seldom shy away from major international stories that cast Russia in an unfavourable light.
The ICIJ report was released late on Sunday night in Moscow, missing print deadlines for newspapers.
But the ICIJ's Russian partner, the opposition newspaper Novaya Gazeta, featured a seven-page hard copy report and a large online version on its website. Since then, most of the popular online news sources have included reports on the story.
There has been plenty of chatter on social media. The hashtag #panamapapers has been in and out of the Top 10 Twitter trends for Russia since Sunday evening.
It seems the story has underwhelmed many Russian bloggers, who were not surprised to learn about potential large-scale corruption. There have been plenty of sarcastic jokes about the alleged sums involved.
In Germany, Munich's Sueddeutsche Zeitung - which originally received the documents - has the online headline "Putin's rich friends - the trail of the secret money".
The heavyweight Frankfurter Allgemeine Zeitung says "Panama's state prosecutors investigate offshore firms", while Berlin's Die Welt reports on "The billion-dollar trails of a global affair".
The tabloid Bild says "Data leak reveals shady transactions worth billions".
China's press is quiet on allegations that the Panama Papers involve Chinese nationals, partly because it is a national holiday, the Qingming Festival.
News outlets have reported the story, omitting any mention of China being involved.  However, it appears that dialogue on the papers is now being censored, as features on the Sina and NetEase web portals have been removed.
There are indications that Weibo social media users want to talk about it, with thousands of posters attempting to discuss the story using the hashtag #PanamaPapers.
Weibo shows that more than 2,000 users have used this hashtag, but posts using it appear currently unavailable to view.
A search of "Panama" on verified media accounts brings up no results, suggesting that the microblog's moderators wish to limit people from searching for this term.
Independent Hong Kong papers, meanwhile, highlight the involvement of the families of a senior Chinese official and a prominent figure.
Arabic news websites and online version of dailies have picked up the story, although regional TV channels have yet to report on it.
Egyptian dailies are leading with revelations about the family of former President Hosni Mubarak.
On Twitter, the hashtags #PanamaDocuments in Arabic and #PanamaLeaks in English have been used in tens of thousands of tweets, trending in Egypt within 12 hours.
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. You can follow BBC Monitoring  on Twitter and Facebook.
Media from Moscow to Beijing are reporting the Panama Papers leak, with some outlets omitting names of local politicians and prominent figures who figure in them.