More than £1m has been raised after the craze of taking a self-portrait with no make-up spread virally.
But those texting "DONATE" rather than "BEAT" found their money sent to the wrong charity.
Others accidentally enquired about adopting a polar bear from the World Wildlife Fund (WWF).
UN agency Unicef told the BBC that so far £18,625 has been identified as being accidentally pledged.
It said it was now working with Cancer Research UK to transfer the funds donated so they can be used as intended.
Mike Flynn, director of individual giving at Unicef UK, said it was a "genuine mix-up".
"Unicef believes this error has occurred due to those interested in donating to the #nomakeupselfie campaign sharing the text keyword 'DONATE' - rather than the keyword 'BEAT' - and the text number 70099, which has then been repeated across social media.
"'DONATE to 70099' is an SMS keyword and shortcode combination that Unicef have sole use of, specifically for any members of the public who contact us and wish to donate to us via SMS."The origin of the #nomakeupselfie trend is unclear
He added: "Unicef 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 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."Adopting polar bears
The #nomakeupselfie craze has taken social media by storm since flourishing last week. Its origins are unclear, but since going viral the trend has raised more than £2m for Cancer Research UK and other cancer charities.
But it has not been without mishaps for some well-meaning selfie takers.
As well as the Unicef mix-up, the World Wildlife Fund (WWF) acknowledged that it too had accidentally received text messages due to the wrong keyword.
Some people's smartphones had autocorrected the word "BEAT" to instead read "BEAR".
"Thank you for choosing an adorable polar bear," the reply from the WWF said. "We will call you today to set up your adoption."
The autocorrect blunder surprised many who took to Twitter to joke about their adoption news.
"Just told Jamie to text 70007 for cancer and he accidentally sent bear," wrote Twitter user @ChrisKirk07. "Now he's got two polar bears."
The WWF said no money was taken from people who had sent the texts.
"Any texts sent to us instead of Cancer Research [UK] 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," said Kerry Blackstock, WWF's director of fundraising.
"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 UK 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."
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