Media reports said Kaur could be fined 75 per cent of her match fee and is also in danger of a two-game suspension for her behaviour in the one-day international, which ended in a rare tie on Saturday.
Kaur hit the stumps after being given out on 14 and later said the umpiring was "pathetic."
She was then heard telling her opposite number Nigar Sultana to invite the umpires on stage after the post-match presentation, forcing the Bangladesh players to opt out of a joint photo session.
"I have been watching cricket for a long time, but have never seen anyone behave that way India skipper Harmanpreet Kaur did after the game," 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. I say that because juniors look up to seniors and this, over a period of time, can impact the team culture," 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. BCCI (Board of Control for Cricket in India) should take very strict disciplinary action."