Cardinal Toppo received a letter demanding the payment of 50 million rupees (around £495,000) that threatened death if the fee was not paid.
It was sent in the name of the People's Liberation Front of India (PLFI), a breakaway faction of the Communist Party of India.
However the police have stressed the suspect has no known connection with the group.
Police have said the suspect identified another man in the letter, known only as Amit, and believe that the accused wished to settle a personal score.
Jaya Roy, Superintendent of Police in Ranchi, said he "mentioned Amit's name and telephone number in the letter so that Amit would face police investigation and arrest," according to UCA News.
It has also been reported that the police are investigating any other links the suspect might have to criminal activity.
Cardinal Toppo acknowledged receipt of the death threat but said he did not know why the group would have any reason to threaten him.
He first became a cardinal in 2003.
