Investigators traced the suspect to the western city of Mumbai and detained him on Wednesday night, the police official told AFP on condition of anonymity.
“He was picked up from a hideout in Mumbai on Wednesday night,” he said.
“He is being brought to headquarters of the investigating agency in Kolkata.”
The nun, who is in her 70s, needed surgery after she was attacked earlier this month when a gang of robbers broke into the convent school in the eastern state of West Bengal where she lived.
Police in the state capital Kolkata identified four of the six robbers through CCTV footage and had detained eight people for questioning.
But no arrests were made until Wednesday and authorities in Kolkata had faced criticism over the pace of progress in the investigation.
Last week, the West Bengal government said it was handing over the case to the country’s top investigators after coming under fire over the lack of arrests.
The assault was the latest in a string of high-profile rapes in India and added to the fears of the country’s Christian minority following a spate of attacks on churches.
Detectives have posted a reward of 100,000 rupees ($1,600) for any leads on the suspects.
Hindu nationalist Prime Minister Narendra Modi has promised a crackdown on religious violence and has said he was deeply concerned about the attack on the nun.
Police have launched a gang-rape inquiry, although officers say only one person sexually assaulted the nun. -AFP