BCCI secretary Niranjan Shah said matters were going "out of hand and going too far."
He said sledging has set a bad example for young cricketers and the ICC had recently discussed the issue. They are considering a ban on sledging and empowering the on-field umpires to slap penalties on errant players.
"We don't want to react and make a controversy in this matter. It is best to ignore such comments which are not good for the game," Shah told NDTV.
Former India cricketer Ajay Jadeja said it was best to ignore sledging.
Speaking on Brisbane radio, Hayden said "It's been a bit of a long battle with Harbhajan, the first time I ever met him he was the same little obnoxious weed that he is now.
Shah said the ICC "had recognised this problem that the youngsters are learning bad things and it is getting too frequent, which is not good for the game."
He said the world body has to discuss what measures need to be taken to settle the issue.
"We have proposed that there should be no unnecessary talk with opponents on the field and umpires should be given more power and there should be stricter penalties," the BCCI secretary said.
Shah said the BCCI always advises the Indian players to exercise restraint and not lose control.
Meanwhile, BCCI vice-president Rajiv Shukla said it was up to the Indian team management to take a view on Hayden's comments.
"So, the team management will definitely get into it. They will take a view and then they will let us know," Shukla said.
He said the remarks had shown Hayden in poor light.
Asked if the Indian players should opt for "eye-for-an-eye" policy against the Australians, Shukla said "I would appeal to them not to do that because a series is going ahead in a very conducive atmosphere. And I think the game must go on".
Comments by one or two individuals should not affect the game, he said.
(With inputs from PTI)