Force India boss Vijay Mallya was arrested in London on Tuesday.
The news follows the Indian government's attempts to have the former billionaire extradited on corruption and fraud charges relating to huge debts.
India's Hindustan Times newspaper claims that the 61-year-old was bailed on a £650,000 bond "within hours".
An Indian politician was quoted as saying: "Will it take another dozen years, 15 years, 30 years or our entire lifetime before Mallya is brought back?"
The Indian government revoked Mallya's passport last April.
