"Indeed. There is no place for corruption in India. Those who looted the poor & middle classes will have to return what they have looted," he tweeted.
He was responding to a tweet by a follower who wrote that "...corruption not only robs us of hard earned money but also of our dignity."
Mr Mallya, who has been declared a proclaimed offender, was arrested in London by Scotland Yard on India's request for his extradition in a loan default case. Senior Indian officials described his arrest as the first salvo in the case, which will now involve a legal process in the UK to determine if Mr Mallya can be extradited to India to face charges in Indian courts.
In response to another tweet, Mr Modi wrote, "India's farmers are the nation's pride. Their hardwork feeds millions. We are doing everything possible for their welfare."