The animal, called Babli, and its owner Abdul Hassan were taken into custody in Chhattisgarh state after the judge, who is a neighbour, filed a complaint to police.
Mr Hassan has been charged with damaging and destroying other's property and trespass - and faces over two years in prison if proven guilty.
Judge Hemant Ratre had been angered by the goat's trespassing and issued an arrest order as officers sprang into action.
He claimed the black goat often scaled the boundary wall and devoured flowers and vegetables on his property.
The female animal and its owner faced charges of causing mischief and damage to property but were later released on bail.
Mr Hassan has admitted the goat's guilt and promised the animal would not damage the garden again.
"My goat has been brought to the police station. It ate up the flowers and vegetables on the lawn of the judge," he said.
TV footage showed the goat now tethered to stop it escaping.
Assistant sub-inspector R Srivastav said: "The goat's owner has been told several times by the judge's representative not to let the animal graze on other people's lawns.
"The goat would eat up all the plants. We received a written complaint from the judge's office on the basis of which we have registered a case.
"An investigation is on and the goat has been arrested."
Another officer Ram Sewak Paikra later said: "The goat and the owner were under police custody and are out, as both the sections 427 and 447 of the IPC (Indian Penal Code) are bailable offences."
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