Police said the Republic TV founder was being investigated for his alleged role in the death of an architect who designed his studio.
Anvay Naik took his life in 2018 and his wife accused Mr Goswami of not paying his fee.
Mr Goswami and Republic TV network deny the allegation.
Mr Naik and his mother were found dead in May 2018 at their home in Alibaug region of the western state of Maharashtra. Mr Naik’s wife said he left a suicide note in which he blamed Mr Goswami for his death.
She has been campaigning on social media for the case to be investigated thoroughly. Maharashtra Home Minister Anil Deshmukh recently ordered a special team to investigate the case.
A police team arrested Mr Goswami from his home in Mumbai on Wednesday. Images showed scuffles taking place between Mr Goswami and the police team.
Republic TV has accused the police of “manhandling” Mr Goswami’s family members – police are yet to comment on the allegations.
Mr Goswami is known for his aggressive style of anchoring and questioning. But his critics say that he often comes across as sympathetic to right-wing politics in the country.
Listen to Anvay Naik’s wife pleading for justice. This is the suicide abetment case in which #ArnabGoswami has been arrested today. Each of us should demand justice for Anvay Naik.
Listen to Anvay Naik's wife pleading for justice. This is the suicide abetment case in which #ArnabGoswami has been arrested today.
Each of us should demand justice for Anvay Naik. pic.twitter.com/PnEvJbKDLE
— Ruchira Chaturvedi (@RuchiraC) November 4, 2020
Well done @CPMumbaiPolice . People like arnab goswami have gutter mouth. We have to stop them before they spread germs in our society. #karma #arnabarrested #WeAreWithMumbaiPolice https://t.co/tpyxaKMVIx
— lalit masurkar🇮🇳 (@lmasurkar70) November 4, 2020