The party's politburo member said instead of celebrating inter-caste and inter-community marriages as "symbols of India's open and liberal approach", there was a campaign against them.
"The NIA is on a fishing expedition having already interrogated 89 such couples in Kerala," Ms Karat said in the latest issue of party organ 'People's Democracy', while referring to the Hadiya case.
She was critical of the central agency's role in probing such marriages, referred to as "love jehad".
"An agency whose proclaimed mandate is to investigate offences related to terrorism has now expanded its mandate by order of the Supreme Court to unearth so-called conspiracies of Muslim men luring Hindu women into marriage and forcibly converting them with the aim of joining the Islamic State (ISIS)," she said in the article.
The underlying assumption, she said, was that Hindu women who married Muslims had "no minds of their own".
"Her (Hadiya's) case reveals how deeply the current climate created by sectarian ideologies based on a narrow reading of religious identity has pushed back women's rights to autonomy as equal citizens. From the government to the courts, to the strengthening of conservative and regressive thinking and practice, it's all out there in Hadiya's case," Ms Karat wrote.
She also hailed Hadiya's unequivocal stand in court. "It was the courage of her conviction that stood out. She wanted to be treated as a human being. She wanted her faith to be respected. She wanted to study. She wanted to be with her husband. And, most importantly, she wanted her freedom," the former Member of Parliament said.
Ms Karat said she appreciated the Supreme Court "for not allowing itself to be converted into a khap panchayat" and charged the NIA counsel supported by the legal counsel of the Central government with portraying it as a case of "indoctrination and brainwashing in a conspiracy of 'love jehad' which they claimed rendered Hadiya incapacitated and invalidated her consent".
The Left leader emphasised that Hadiya's case brought into focus the right to practise and propagate the religion of one's choice under the Constitution.
Ms Karat expressed the hope that the apex court would "act in a way which strengthens women's rights unencumbered by subjective interpretations of tradition and communal readings of what constitutes national interest".
Hadiya had said in the apex court last week that she wanted to go with her husband, Shafin Jahan.
The 24-year-old Kerala woman had converted to Islam, changing her name from Akhila to Hadiya, and married Shafin Jahan The marriage was challenged by her parents in court.
Shafin Jahan moved court after their marriage was annulled by the Kerala high court and against the high court court's order directing the NIA to probe the case.
The Supreme Court last week allowed Hadiya, till now in the custody of her parents, to resume her studies at a homoeopathy college in Salem, Tamil Nadu.