The Indian government has intervened in the controversy over an Australian marketing campaign for lamb, lodging an official diplomatic complaint.

The Indian high commission in Canberra has made a "demarche" to three government departments - Foreign Affairs, Communications and Agriculture - over the Meat and Livestock Australia ad that features the Hindu deity Ganesha eating lamb.

The ad that was meant to promote inclusivity has backfired by angering Australia's Hindu community, who call it "ignorant and insensitive".

It features religious figures such as Jesus, Buddha, Scientology founder L. Ron Hubbard and Greek goddess Aphrodite enjoying a lamb lunch. Ganesha is depicted digging in despite being considered vegetarian by followers of the religion.