The arrests were ordered on Friday by the state assembly for "breach of privilege" in articles and an editorial about Chief Minister Jayalalitha Jayaram's administration.
A two-judge bench of the Supreme Court said "every institution, be it the legislature, media or judiciary, has to respect other institutions".
"None of the institutions should cross the fine line or be hyper-sensitive to harsh words of criticism," the judges said.
Five journalists from The Hindu - a national daily - were targeted by the assembly after the publication accused the state government of "rising intolerance towards political opponents".
The editor of the Tamil-language daily Murasoli was given the same sentence for publishing a translation of The Hindu editorial.
On Friday night, police went to The Hindu's headquarters in the southern city of Chennai and searched the offices of top editors, but did not make any arrests. The six journalists had apparently gone into hiding.
The Hindu's editor-in-chief N Ram said he was "delighted" with Monday's court ruling.
"None of the institutions should cross the fine line or be hyper-sensitive to harsh words of criticism"
"Our confidence in the Supreme Court and highest judicial forums has not failed us," he said.
"I stand for the cause of press freedom and I thank all who stood with us," he added.
Deputy Prime Minister Lal Krishna Advani described the verdict as "good for democracy".
Earlier, a delegation of opposition MPs and legislators from Tamil Nadu met Advani to register their protest at the sentences.
The ruling Hindu nationalist Bharatiya Janata Party (BJP) and the main opposition Congress party have also said the Tamil Nadu authorities acted improperly.
Media groups across India expressed outrage at the sentence, with one group of reporters in New Delhi burning an effigy of Chief Minister Jayalalitha.
Journalists, wearing black ribbons, held a sit-in protest at a press club in the western desert state of Rajasthan and similar protests were reported from the northern states of Punjab and Uttaranchal.