During the one-day international match against Bangladesh, Kaur displayed her frustration by hitting the stumps after being given out on 14. The match ended in a rare tie. Later, she expressed her dissatisfaction with the umpiring, referring to it as "pathetic."
"I have been watching cricket for a long time, but have never seen anyone behave that way," former women's captain Diana Edulji wrote in her column in the Indian Express on Tuesday.
"She has set a bad example for her teammates," Edulji said.
"It was deplorable to see Harmanpreet call the umpires to pose with the Bangladesh team, suggesting that they were part of the team and playing for them."
Indian men's World Cup winner Madan Lal also blasted Kaur.
"Harmanpreet's behaviour against the Bangladesh women's team was pathetic," Lal tweeted.
"She is not bigger than the game. She got a very bad name for Indian cricket."
India's own cricket authorities "should take very strict disciplinary action", he added.
India Skipper Harmanpreet Kaur expressed her strong displeasure with the umpiring standards after the thrilling tie between India Women and Bangladesh Women in the third One-Day International at the Shere Bangla National Stadium in Mirpur on Saturday.">