The Corporation also apologised to relatives of Fr John Gerard after the 'Elizabeth I's Secret Agents' programme said he gave the conspiracy "God's blessing".
In a letter seen by the Daily Telegraph, bosses said that "presenting his foreknowledge as settled fact was seriously misleading".
The BBC Two documentary, which was made by 72 Films and was first aired last October, shall be altered before it is re-broadcast.
The admission comes after the priests' ten times-great nephew, Michael Maslinski, complained to the BBC and argued for the Jesuit's innocence.
'Elizabeth I's Secret Agents' states that Guy Fawkes and his fellow co-conspirators met Fr Gerard in London before the plot which was foiled better it could be realised.
He was quoted by the Telegraph as saying: "John Gerard has been revered in my family for 400 years... To see him represented as a terrorist was shocking".
A previous complaint of a similar nature levelled by Mr Maslinkski against the BBC One drama 'Gunpowder' was dismissed by the Corporation on the grounds of dramatic licence.
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