A spokesperson for the department for culture, media and sport said the temporary ban followed the advice of the reviewing committee on the export of works of art and objects of cultural interest (RCEWA).
The government said the committee highlighted the bust’s “aesthetic importance” and “outstanding significance” to the study of 18th Century sculpture in Britain and Europe.
The decision on the export licence application has been deferred until 8 April so that any offers can be made.
A spokesperson for Invergordon Museum said the government’s intervention was a “vital victory” for local and national heritage.
The heritage centre said it hoped to display the bust locally in a new facility.
Highland Council declined to comment on the temporary export ban because of the “ongoing process”.