He is being investigated over allegations that he cleared foreign investments in exchange for bribes while he was finance minister.
Mr Chidambaram, 73, has denied the allegations.
A senior member of the main opposition Congress party and an MP since 1984, he has also served as home minister.
He was arrested by the Central Bureau of Investigation (CBI) on Wednesday evening amid chaotic scenes as supporters and media surrounded his car while being driven away.
The night before, officials arrived at his home in capital Delhi to question him, but said he was not at home.