In the episode, broadcast on Wednesday, Sir David told viewers: "Some parts of the continent have become 3.5C hotter in the past 20 years", but the BBC has since admitted that is "disputable".
The line was removed from the repeat episode and the re-edited version has replaced the original show on the iPlayer.
A BBC spokesman said: "There is widespread acknowledgment within the scientific community the climate of Africa has been changing.
"We accept the detail is disputable and the commentary should have reflected that, therefore the line of commentary has been edited out of Sunday's repeat and iPlayer version removed."
It has been reported the mistake was made by the production team and not by Sir David, who told them he did not know how it ended up in the script.
The BBC had earlier defended the figure, at first saying it came from a report by Oxfam and the New Economics Foundation – which referenced earlier research by Christian Aid – but issued the statement yesterday following growing disquiet among environmental experts.
It is not the first time Sir David's award-winning natural history shows have run into trouble in recent years.
In 2011, the veteran broadcaster had to defend using footage in his Frozen Planet series of a polar bear tending her newborn cubs that was shot in a German zoo.