It wanted to "restore dignity back to the statue", a spokesman told the BBC.
The sculptors reportedly inserted the rabbit as a trademark signature and to denote the haste with which they had to complete the statue.
Rabbit in the Afrikaans language is "haas", which also means haste.
"We don't think it's appropriate because Nelson Mandela never had a rabbit on his ear," Mogomotsi Mogodiri, the spokesman for the Department of Arts and Culture, told the BBC's Focus on Africa radio programme.
"We'd want people to see that statue as a symbol of hope, not about something like a rabbit."
