Cricket Australia chief executive James Sutherland released a strongly worded statement on Monday after Hair was voted off the elite panel before his contract had ended.
Sutherland said Saturday's decision, which has divided world cricket, had undermined public confidence in umpires and an urgent review was required into the procedures used to oust him.
"We don't agree with the ICC's decision and are concerned about the implications which could see international umpires concerned about off field consequences of calling decisions as they see them," Sutherland said.
"World cricket needs champion cricketers, but it also needs world-class umpires who are equivalently skilled at what they do.
"To aspire to these heights, those umpires need to have confidence in the system -- that they are supported by best-practice administration and processes."
Hair was sacked after Pakistan lodged a complaint over his role in the forfeited Test against England and the ICC voted 7-3 to remove him.
The decision was largely applauded in the subcontinent but drew an angry response in Australia with former players describing the move as "tragic" and "disgusting".
Sections of the Australian media complained that the decision would have serious long-term repercussions for the game because umpires would be frightened of making decisions that offended the Asian bloc nations.
Sutherland said Cricket Australia regarded Hair as one of the best umpires in the world and would welcome him back to umpire in the first-class interstate competition.
