The episode, which has been described as including "every Dalek ever", was named in the Institute's advance programme. The screening will include a Q&A session with writer and show runner Steven Moffat plus other members of the cast and crew yet to be confirmed.
Tickets go on sale to the public from 10th July (BFI members from 3rd).
As previously reported, the episode will also be shown at the MediaGuardian Edinburgh International Television Festival, which runs from 23rd to 25th August.
The television premiere of the episode has yet to be announced; however, last year's Let's Kill Hitler received both a BFI and MGEITF premiere in August prior to its broadcast on the Bank Holiday weekend, which for this year would be Saturday 25th August.
Speaking on the BBC's Doctor Who website, executive producer Caroline Skinner said:
This is an epic Dalek adventure that kicks off the new series in explosive style! If you think you know all there is to know about the Daleks, think again...