A picture of four men wearing turbans posing in a corridor was posted on the governing body's Twitter feed with the caption: "Will the real Monty Panesar please stand up?!"
The post drew a number of negative responses, including from former England captain Michael Vaughan who tweeted: "Awful from @CricketAus".
Cricket Australia deleted the post and said: "We apologise for any offence caused with our previous tweet. That was certainly not the intention. It has been removed."
The gaffe follows the dismissal of a ground announcer during last week's tour match in Alice Springs between England and a Chairman's XI for allegedly introducing Panesar with a mock-Indian accent. The announcer later denied any wrongdoing.
Panesar, whose parents are of Indian heritage, was named in Alastair Cook's team as a second spinner along with Graeme Swann at Adelaide Oval.
Australia lead the five-Test series 1-0.
Image: Monty Panesar
Photograph: Gareth Copley/Getty Images