The tourists called a halt after the spinner was suspended for three games for making a racist comment to Andrew Symonds in the second Test in Sydney.
Harbhajan is available until his appeal, which could take place before the third Test in Perth on 16 January.
Umpire Steve Bucknor, who angered India with his decisions in Sydney, has been replaced for that game by Billy Bowden.
India will now move on to Canberra, where they play a warm-up match on Thursday ahead of the third Test.
But the furore could erupt again if match referee Mike Procter's decision to penalise Harbhajan for allegedly calling Symonds - the only non-white player in Australia's team - a "monkey" is upheld.
International Cricket Council chief executive Malcolm Speed said a commissioner will be appointed by Wednesday to hear the appeal.
In a statement the Board of Control for Cricket in India called the ban "totally uncalled for, unjustified and patently illegal" and said it would "take all possible steps...to get the player cleared of the obnoxious and baseless accusation".
It added: "The ICC has clarified to the board that Harbhajan could play until the final disposal of the appeal.
"This is only an interim arrangement. The BCCI is of the categorical view that the matter will have to be finally resolved and the unfair allegation against an Indian player be set aside or withdrawn.
"The BCCI will review the tour and all other developments continuously."
Meanwhile, the fallout of the tempestuous Sydney Test continued with the news that Australia spinner Brad Hogg has also been charged with making an abusive remark to India captain Anil Kumble and his deputy Mahendra Dhoni.
The ICC earlier made a move which appeared to calm the situation by replacing Bucknor.
The Jamaican official came under fire for a series of controversial decisions as India lost by 122 runs to go 2-0 down in the series.
His removal represented a U-turn by the ICC, which initially said on Monday that the Jamaican would be retained even though the Indians had made a written complaint over his "incompetence".
But Speed said the ICC had not acted on India's insistence.
"It is accepted that Steve, and his on-field colleague Mark Benson, did not have good games by their very high standards," he admitted.
"We feel that given the added pressure and attention Steve's presence would have at the third Test, it is better for the match and for Steve himself if he does not take part.
"It is important to stress that Steve has not been replaced due to any representations made by any team or individuals.
"The ICC remains the sole body responsible for the appointment of umpires and no team has the right to object to any appointment."
Bucknor, 61, is the most experienced umpire in international cricket history, having stood in a record 120 Tests, and five World Cup finals.
Although there were decisions that went against Australia in Sydney, the Jamaican was guilty of two major errors against India that went on to have a major impact on the course of the match.
On the first day Australian all-rounder Andrew Symonds was incorrectly given not out on 30 before going on to making an unbeaten 162.
And on the last day, India's Rahul Dravid was wrongly given out when he was battling to save the game.
The ICC also announced that chief referee Ranjan Madugalle has been appointed to act as a mediator in the row between Australia captain Ricky Ponting and Anil Kumble.
After the Sydney defeat, an angry Kumble claimed that "only one team was playing within the spirit of the game".
And Speed said: "We are bringing Ranjan in as a facilitator in an effort to prevent any ill-feeling that may have been present at the Sydney Test from rolling over to Perth."
The actions of the Australian team in Sydney have led to fierce criticism back home, with Ponting's role in the game coming under intense scrutiny.
The Sydney Morning Herald has called for Ponting to be dismissed, saying that Cricket Australia should not tolerate the "arrogant and abrasive conduct seen from the captain".
And an online poll in Australian newspaper the Daily Telegraph 79% of respondents said the team did not play in the true spirit of the game while 83% said Ponting was not a good ambassador for the game.
BBC News Sydney correspondent Nick Bryant said: "The Aussies love winning but they like winning well, and there's a feeling after 16 straight Test victories that Ricky Ponting's team has just gone too far in the aggressive way in which they play."
But Ponting has been defended by batsman Mike Hussey, who told the Daily Telegraph that the skipper "has got the full support of everyone in our team".
"I think he is the best captain I have played under," added Hussey. "We go out to play the game as hard as we can but also as fairly as we can. Ricky is very big on that."
Ponting has defended his decision to report Harbhajan during the second Test.
He told The Australian: "Over the past two years match referees have made it clear at the start of every series that it is the captain's responsibility to immediately report any form of racism from either the crowd or on the field.
"When I heard what had taken place with Andrew, I immediately informed the umpires and then left the field at the end of the over to inform our team manager, which is what we are instructed to do."Making this report is not something I wanted to do but something I had to do. I had nothing to gain personally from taking this action. I was doing the right thing by the game.