The channel named the pro-jihad tweeter "@ShamiWitness" as "Mehdi", but did not reveal his full name as he said his life would be in danger.
"He is an executive in Bangalore working for an Indian conglomerate," the channel said on Thursday.
The report quoted him as saying that he had not joined IS jihadist ranks in Iraq and Syria because his family was financially dependent on him.
"If I had a chance to leave everything and join them I might have," he was quoted as saying.
The account, which had 17,700 followers including many foreign fighters, was shut down following the Channel 4 report.
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Indian police told reporters they were investigating.
"I have seen the report as you have," Bangalore police commissioner M.N. Reddi said at a media briefing on Friday.
"We have taken note of it and are investigating the matter.
"We are ready to face any threat perception to the city. We have set up a special team to study the report and trace the culprit," he said.
The Shami Witness tweets contained jihadist propaganda as well as information for would-be recruits and messages praising fallen fighters as martyrs.
The IS militant group has made extensive use of social media for propaganda and recruitment, as well as for disseminating grisly execution videos.