The Chief Minister said she had learnt that two office memoranda issued by the Union Home Ministry "direct that official accounts on social media like Google, Facebook, Twitter, blogs, YouTube which at present use only English, should compulsorily use Hindi, or both Hindi and English, with Hindi being written above or first."
That makes the use of Hindi mandatory and English optional, she said in the letter.
"As you are aware, as per the Official Languages Rules, 1976, communications from a central government office to a state or Union Territory in Region "C" or to any office (not being a central government office) or person in such state shall be in English."
"This provision has been introduced following the introduction of a mandatory proviso in Section 3(1) of the Official Languages Act, 1963, by an amendment in 1968 which states (that), 'English language shall be used for purposes of communication between the Union and a state which has not adopted Hindi as its official language," she pointed out.
Social media by its very nature is not only accessible to all persons on the Internet but is meant to be a means of communication between people across India, including those in "Region C", Jayalalithaa said.
"People located in "Region C", with whom the government of India's communication needs to be in English, will not have access to such public information if it is not in English. This move would therefore be against the letter and spirit of the Official Languages Act, 1963," she said.
Jayalalithaa added it was a "highly-sensitive issue and causes disquiet to the people of Tamil Nadu who are very proud of and passionate about their linguistic heritage".
"Hence, I request you to kindly ensure that instructions are suitably modified to ensure that English is used on social media," she told Narendra Modi.
Further, recalling a memorandum she had presented to him on June 3 during her Delhi visit, Jayalalithaa reminded Modi about Tamil Nadu's demand for making Tamil an official language of India.
She recalled she had sought that all languages listed in Schedule VIII of the Constitution be given that status and had said that "if this request is fulfilled, the use of all official languages on social media can be encouraged."
Tamil Nadu had witnessed an anti-Hindi agitation in the late 1960s and DMK chief M Karunanidhi, whose party had spearheaded that movement, has also opposed NDA government's latest proposal, saying it was the beginning of the "imposition of Hindi".