According to a statement from the International Cricket Council, the ICC has to appoint an appeals commissioner within two days, who then has seven days in which to hear the appeal.
The Gibbs affair has been front page news in South Africa and the player has received public support after being heard making racist remarks about Pakistan supporters.
A poll in The Star newspaper found that 78 percent of people felt Gibbs' ban was unjustified and only 22 percent thought it was fair.
The SA Cricketers' Association has leant its full support to Gibbs.
Chief executive Tony Irish said: "It is not appropriate for us to deal publicly at this stage with the merits of the appeal before the ICC.
"However I can confirm that we are now awaiting the written statement from the match referee and the appointment of an Appeals Commissioner as provided for in the ICC Code of Conduct."
Meanwhile conflicting reports of the incidents which led to Gibbs' remarks have been published in South African newspapers.
The three spectators who were moved from seats near the boundary after allegedly swearing at bowler Paul Harris claim that Harris swore at them.
But other spectators say the Pakistani supporters were abusive and made watching the game unpleasant for people sitting near them.
Gibbs' father, meanwhile, has accused the ICC of looking away when South African players were victims of racist remarks in Australia last year.
"There are a bunch of incorrigible old men in the ICC," Herman Gibbs senior told the South African SuperSport website.
"They were unable to do anything about match fixing and are too afraid to tackle any controversial matter properly."
Herman Gibbs said his son was not in the slightest bit racist despite the finding by match referee Chris Broad that his comments overheard on television were "racially offensive".
A Cricket South Africa hearing into Gibbs' conduct has been postponed pending the outcome of his appeal to the ICC.