The 30-minute film, which calls for the Ugandan rebel leader to be arrested, had attracted more than 15 million views by Thursday, just three days after it was uploaded.
A hashtag promoting the video was also trending worldwide on Twitter, with US celebrities Rihanna and P Diddy and Australian cricketer Shane Warne among those posting links to the film.
KONY 2012 was posted by Invisible Children, a US non-profit organisation based in San Diego, California, but with offices in northern Uganda, where Kony's Lord's Resistance Army has waged an armed campaign for more than two decades.
Kony, who started an armed rebellion against the Ugandan government in the late 1980s, has been accused of abducting and forcing children to join the LRA, charges that led to his indictment by the International Criminal Court in 2005.
The film opens with the statement: "Nothing is more powerful than an idea whose time has come." The video depicts the use of child soldiers in conflicts and the suffering they have to endure.
Although 802,562 viewers said they liked the video, 23,483 said they did not - and the success of the film has caused Invisible Children's work to face scrutiny.
On its website, Invisible Children says it "uses film, creativity and social action to end the use of child soldiers in Joseph Kony's rebel war and restore LRA-affected communities in central Africa to peace and prosperity".
The group has been accused of spending much of the money it raises from donors on staff renumeration and filmmaking, and Navigator, a US watchdog charity, has previously given it two out of four stars for financial transparency and accountability.
One viewer of the film posted that people should "think twice before donating to KONY 2012".
Group defends work
Jolly Laker, Uganda country director for Invisible Children, told Al Jazeera local leaders in northern Uganda had been impressed by work done by the group.
"When you talk to local leaders, you will know how much our work has affected people," she said. "Two days ago, government leaders commended us for our work. You can only see our work when you're on the ground."
In a blog responding to criticism, Invisible Children said it had received hundreds of thousands of comments in support of the Kony's arrest, but said the film had also provoked "false or misleading information" about its work.
It said it had spent 80.46 per cent of its funds on programmes furthering its mission, and said Navigator had given its programmes the highest ranking of four stars.
It said its two-star accountability rating was due to the fact it had only four independent voting members on its board of directors, rather than the required five. It said it would add an additional member by 2013.
"Invisible Children’s financial statements are online for everyone to see," the statement said.
The group said the KONY 2012 campaign was calling for US leaders to help remove impediments to Kony's arrest in countries where he has operated.
"The campaign also advocates for broader measures to help communities being affected by LRA attacks, such as increased funding for programmes to help Kony's abductees escape and return to their homes and families," it said.
Although the LRA is considered to have been severely weakened in recent years, with many of its commanders killed in combat, Kony has eluded arrest and has not been seen in public since 2006.
Last October, US President Barack Obama said he was deploying 100 "combat-equipped" troops to Uganda to help efforts against the LRA.
The US troops, subject to the approval of national authorities, were to deploy from Uganda into South Sudan, the Central African Republic and the Democratic Republic of Congo, Obama said in a message to Congress.
Obama said the US troops would act as advisors to local forces with the goal of removing Kony and other senior leaders from the battlefield, and would not lead the fighting themselves.