The craze has seen soaring numbers of women posting pictures of themselves wearing no make-up on social media sites and nominating their friends to do the same.
Cancer Research UK, which did not start the campaign, said the #nomakeupselfie trend had resulted in an "unprecedented increase" in donations after it received £8 million in six days.
But it has emerged that some people intending to donate to the charity sent their cash to Unicef in error, while others had mistakenly enquired about adopting a polar bear with the World Wildlife Fund (WWF).
Cancer Research UK and Unicef use the same text number for donations but those texting the keyword "DONATE" rather than "BEAT" found their money sent to the UN agency.
Mike Flynn, director of individual giving at Unicef UK, said there had been a "genuine mix-up" and it was working with Cancer Research UK to transfer £18,625 which was donated by mistake.
He said: "Unicef UK is not responsible for this error, however we've been working hard to find a resolution to the situation for those affected.
"We contacted Cancer Research UK as soon as we became aware of what was happening. Unicef UK and Cancer Research UK have agreed that these donations will be received in full by Cancer Research UK.
"We are now working closely with all parties involved to ensure that this doesn't happen again in the future."
The WWF confirmed that it too had accidentally received text messages due to the wrong keyword.
Those texting the word "BEAR" instead of "BEAT" meant they had enquired about adopting a polar bear through the charity.
The WWF said no money was taken from people who had sent the texts.
Kerry Blackstock, the charity's director of fundraising, said: "Any texts sent to us instead of Cancer Research would not result in any donations going to help protect polar bears as WWF relies on human operators calling people back to confirm adoptions, so no money would have changed hands.
"When we realised there was a lot of interest in a campaign we weren't presently running we made sure our automatic text message response let the sender know their text had gone awry.
"We wish Cancer Research every success in their campaign and their goals. Polar bear selfies are harder to come by, though as far as we are aware, none wear make-up."
Carolan Davidge, Cancer Research UK's director of communications, said: "We're really grateful to everyone who donated to Cancer Research UK through the #nomakeupselfie campaign.
"We've agreed with Unicef that the donations they received will be given to Cancer Research UK. People who made a donation in error to Unicef have already been contacted to let them know the money is being transferred."
A host of famous females including US superstars Beyonce and Rihanna, British model Cara Delevingne and X Factor judge Cheryl Cole are among those to take part in the trend across Facebook, Instagram and Twitter.
Cancer Research UK said the donations will allow the charity to carry out 10 clinical trials which it did not have money to fully fund last week.
Harpal Kumar, chief executive of Cancer Research UK, said: "We've been overwhelmed by the support people have been showing us through the #nomakeupselfie trend.
"We don't receive any government funding for our research and so it's phenomenal to think that the generosity of the public is enabling us to fund critical research that we didn't have the money for six days ago. Being able to fund more trials will bring forward the day when all cancers are cured.
"It's been an exciting week, and we'd just like to thank everyone again for their support."