Banerjee, 49, was dragged out of her husband's house by masked gunmen in Afghanistan's eastern Paktika province and shot dead last Wednesday.
"Police have arrested two people who have confessed to killing her," Paktika governor spokesman Mokhlis Afghan told AFP.
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"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.
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