According to an official statement issued Monday, Tandon cited personal reasons for her resignation, stating she found it "increasingly difficult" to balance her current commitments and workload.
She said she wished to resign due to time constraints and other unavoidable circumstances due to which she would not be able to devote the time required to do justice to her duties.
The statement said Information and Broadcasting Minister S. Jaipal Reddy had accepted her resignation.
Tandon, who was appointed to the post in 2003 during the previous National Democratic Alliance (NDA) regime, was accused in November of not attending a single meeting of the CFSI - an allegation she strongly refuted.
Denying that she had neglected her charge, the then pregnant actress cited records to prove she had attended every meeting, but admitted she did not go to office everyday.
Her continuation in the post became controversial since many other NDA-appointees had been eased out after a new Congress-led coalition came to power last year.
A National Award winner, Tandon had been adamant about not quitting before her three-year term was over.