The outdoor poster featured text which read “SOBER AS A MOTHERFU” next to the image of a beer can.
Twenty-six people complained to the Advertising Standards Authority (ASA) about the campaign, which was due to run for two weeks from 21 October.
The ASA ruled that the billboard was likely to cause "serious and widespread offence" as it contained a "clear reference to a swear word" and was not appropriate for display where it could be seen by children.
BrewDog said that the poster was designed to be "eye-catching" and promoted being sober.
The brewer argued that as the advert contained no profanity it could not cause any "serious" offence.
But the ASA has banned the advert in its current form.
"We told BrewDog plc to ensure they avoided causing serious or widespread offence by, for example, avoiding references to expletives in media targeted to a general audience which included children," the ASA said.