It comes after the British network Channel Four said a Bangalore executive ran the Twitter handle @ShamiWitness.
The account, which has since closed, provided news on IS and celebrated its rise in Syria and Iraq.
Indian police have not confirmed the identity of the detained man, who was named as "Mehdi" in the report.
With nearly 18,000 followers, @ShamiWitness was one of the main sources of information about the group in English.
The IS militant group has used social media to recruit foreign fighters and to disseminate videos of their fighters beheading Western journalists and aid workers.
