An inner city council has become the first in Sydney to drop Australia Day celebrations, with its mayor hailing the move as "the right thing to do".

Inner West Council mayor Darcy Byrne said councillors supported a proposal to ditch the celebratory element of January 26, instead encouraging residents to attend the Aboriginal Yabun festival held that day.

As flagged in the Herald last week, the council voted on the proposal on Tuesday night after an online survey showed most people opposed holding a celebratory Australia Day event.

"It's a small but respectful act of recognition. The right thing to do," Mr Byrne wrote on Facebook after Tuesday night's vote.