Orphans, street children, albinos and the disabled are most at risk.
A new Unicef report warns that children accused of being witches – some as young as eight – have been been burned, beaten and even killed as punishment.
The belief that a child could be a witch is a relatively modern development, researchers say.
Until 10-20 years ago, it was women and the elderly who tended to be accused.
The agency says the rise in vulnerable children being abused in this way is linked to greater urbanisation in the continent and disruption caused by war.
The growing economic burden of raising children is also thought to be a factor.
The agency said there was little it could do about the belief in witchcraft itself, and that it was not trying to eradicate the practice. But it said violence against children was wrong, and that it would do everything it could to stop it.
‘Major problem’
Most of those accused of witchcraft are boys aged between eight to 14 – who often end up being attacked, tortured and sometimes killed.
Also, children have had petrol poured into their eyes or ears as a way of trying to exorcise “evil spirits” that healers believe have possessed them.
It is reported that some evangelical preachers have added to the problem by charging large sums for exorcisms. One was recently arrested in Nigeria after charging more than $250 for each procedure.
There has been no comprehensive study to suggest how widespread child witchcraft allegations are.
However Unicef’s Regional Child Protection officer for West and Central Africa told the BBC more than 20,000 streetchildren had been accused of witchcraft in the DR Congo capital Kinshasa.
Joaquim Theis told the Newshour programme that such children had often been beaten and sent away from their homes.
“The children would be forced to admit being witches and then asked to tell the accusers who passed on the witchcraft to them.”
Mr Theis said reintegrating affected children remained a “major problem”.