GCMMF sells its products under the famous Amul brand.
Chaudhary's appeal came up before the division bench of Justice V M Sahai and K J Thakar. However, Justice Thakar recused himself from the case. Chief Justice Bhaskar Bhattacharya will now assign the matter to another bench.
On Monday, a High Court judge had allowed the Federation to implement the no-confidence motion passed against Chaudhary by 14 of the 18 directors after January 11.
In October, 14 out of the 17 member unions of the GCMMF Board had moved a no-confidence motion against Chaudhary who was elected as chairman in August 2012.
Established in 1973, GCMMF is India's largest food product marketing organisation which clocked an annual turnover of USD 2.54 billion in 2012-13.