George wrote a number of tweets, some of which have now been removed, that could have been deemed as offensive to sufferers of domestic violence, before later using the platform to apologise for the comments.
"Paul George's tweets from earlier were thoughtless and without regard to the subject of domestic violence and its seriousness in society," said Bird in a statement released by the Pacers.
"We have talked to Paul to strongly express our displeasure and made it clear that the NBA and the Pacers' organisation will not condone or tolerate remarks of this nature.
"Paul understands that he was wrong and why his tweets were so inappropriate and is very apologetic."
The Pacers will return to action when the new NBA season begins in late October.