Mr Tharoor, 61, had punned on the name "Chhillar" in what he called a light-hearted tweet: "What a mistake to demonetise our currency! BJP should have realised that Indian cash dominates the globe: look, even our Chhillar has become Miss World!"
His reference was apparently to "chillar", Hindi slang for loose change.
A little later, he also put out another tweet admiring the answer that won Manushi Chillar the crown and ended a 17-year dry patch for India at the international pageant.
But Mr Tharoor soon found himself bombarded by disapproving comments over his first tweet.
चिल्लर और छिल्लर में अंतर होता है शशि जी ..मतलब राजनीतिक निशाना साधना हो तो कुछ भी ..हद है— Rishita Mishra (@rishitamishr) November 19, 2017
You said this!!! Unbelievable! Sir, how can anyone at ur stature possibly think like this, leave aside making a tweet.— Nitish Kumar (@nitishcop) November 19, 2017
The National Commission for Women demanded an apology from the Kerala parliamentarian for "degrading a daughter of India". It said: "He degraded the achievement of daughter of #haryana and #India who got glory to the country. Will he call his own daughter chillar? He must apologize immediately."
Mr Tharoor finally tweeted an apology, accepting the assessment of his critics that the pun is "the lowest form" of humour but urging them to "chill".
Guess the pun IS the lowest form of humour, & the bilingual pun lower still! Apologies to the many who seem to have been righteously offended by a light-hearted tweet today. Certainly no offence was meant to a bright young girl whose answer i've separately praised. Please: Chill!— Shashi Tharoor (@ShashiTharoor) November 19, 2017
The women's commission has asked him to apologise "properly", berating him for "telling people to chill".
Among those who attacked Mr Tharoor were two ministers of the BJP government in Haryana, Manushi Chhillar's home state.
"Tharoor has only exposed his own debased thinking by questioning the self-respect of our daughters, the pride of the country, and the brave community 'Chhillar'," Haryana Women and Child Development Minister Kavita Jain said in a statement accusing Mr Tharoor of "indulging in callous and reckless wordplay".
Her colleague Capt. Abhimanyu lacerated the Congress leader for what he called a "shameless comment" that deserves to be withdrawn. "..can't believe...he can go so low...(sic)" the minister tweeted.