"It was never our intention to cause any offence. To say we are gutted would be an understatement."
The brigade was approached but declined to add any further comment "in the near future".
The statement did not detail the complaint's content or origin.
Within an hour of being published, the statement's comments section was inundated with messages of support for the brigade.
A commenter who had seen the video before it was removed told the Otago Daily Times it featured firefighters performing a "mock catwalk" to the Right Said Fred song I'm Too Sexy.
It did not involve anything offensive, apart from "the odd shirt off and a bit of gyrating", she said.
"It was hilarious and they did an amazing job for a totally worthwhile cause... I've known some of the guys a long time and seen a whole new side to them."
She believed people should "get on board" with the video and the cause, rather than criticising the firefighters for trying to help.
One commenter described it as a "harmless bit of fun", another said it was "awesome" and another that those who took offence must have "missed the message".