The interview will be broadcast the morning after the third and final leaders' debate on April 29.
With this slot, the BBC is compensating for Griffin's omission from the first-ever televised debates.
The BBC's chief political adviser has said the BNP should be allowed to feature on Today to ensure fair representation for all political parties.
Senior BBC journalists and presenters are however understood to be furious over the issue. Anti-fascist presenters have also staged rallies outside Television Centre in West London, protesting the move.
Defending its decision to give slots to minority parties, the BBC said it was done to maintain impartiality.