Mr Martin, who shares the same name as the lead singer of the band, tweeted: "To the 500 Indian followers I gained in the last day I'm not in Coldplay."
He also updated his Twitter profile to read, "currently HUGE in India".
He told the BBC that a lot of his new followers are "laughing with me and a surprising amount feel sorry for me".
"A few have pointed out that me and him look similar. I don't see it, but I guess we are both skinny white men with some half baked facial hair," the British comedian said.
Mr Martin has been retweeting some of the more humorous responses he has been getting from India, including one that read: "Why do all white men look the same?"
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He says that despite his clarifications a lot of his followers seem to have stuck around.
"Pity followers I call them. But I'll take them. Since it's been in the media a few have jumped on the bandwagon. Everyone is welcome in my follower crew."
Some of them have even gone to his website and watched his stand-up clips but not everyone is a fan.
"One guy said he didn't find it at all funny but then called me 'buddy'. Quite possibly the politest online troll I've ever had," he said.
Mr Martin has more than 13,000 followers on Twitter.
A comedian named Chris Martin has, to his bemusement, received an influx of Twitter followers from India shortly after a Coldplay concert in Mumbai.