The charity said on Tuesday that it was seeking further clarification as to why Facebook had turned down the RNIB advert, which the charity wanted to be promoted on the social networking site on a paid-for basis.
But in a statement made on Wednesday, Facebook said it had made a mistake and would allow the advert to be promoted through its site.
"Facebook is a place for people and organisations to campaign for the things that matter to them, and the Royal National Institute of Blind People’s video ad is a great example of that," the statement said.
"In this instance we made a mistake and have contacted the charity to let them know and to apologise for any inconvenience caused."
The RNIB advert shows a woman’s face with a voiceover that says: "This is the moment that your doctor says you’re losing your sight. You’ll fear for your job, your home, your life. You’ll be angry that there’s nobody at the hospital who can help you face the future."
It goes on to say that only one in three UK hospitals has a sight-loss adviser and calls on people to demand support.
Natasha Dickinson, group head of marketing and communications at the RNIB, said: "We’re really pleased that Facebook has acknowledged it made a mistake in banning our advert.
"We accept that mistakes sometimes happen and hope that in future Facebook will work more closely with us and other charities to stop this type of situation happening again."