"Police have arrested two people who have confessed to killing her," Paktika governor spokesman Mokhlis Afghan told AFP.
"They have said in their confession that they were ordered to kill the lady because the film that was made from her book was an insult to the Taliban," Afghan said.
"They also said she had Internet in her house and was spying for India," he added.
The two men belong to the Haqqani network, a Taliban affiliate with links to Al-Qaeda, and were arrested in Sharan, the capital of Paktika province late Monday, the governor's spokesman said.
The Taliban last week denied involvement in her murder.
Banerjee was married to local businessman Jaanbaz Khan and had recently moved back to live with him in Paktika, reportedly to run a health clinic for women.
Her book "Kabuliwala's Bengali Wife," which is an account of her escape from the Taliban two decades ago, was made into a Bollywood film in 2003.