TV personality and actress Sharon Au prompted a minor outcry after she approached the girl, who was sitting in the crowd with an older man, presumably her father.
"What (vat) happened, what happened?" she laughed, wobbling her head from side to side, after the girl stumbled as she tried to repeat a line welcoming athletes to the Games.
Au, who is ethnic Chinese, also teased the girl about her name, Kavya, calling her "caviar" instead.
"Some of you may have watched the pre-show and heard my attempt at mimicking an Indian accent," she posted on her Facebook page.
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"It was intended to be comic but in hindsight I realise how insensitive it was. I sincerely apologise to those whom I've inadvertently offended."
Au is a well-known personality in Singapore who has been cast to play the wife of late strongman leader Lee Kuan Yew, who died in March, in "The LKY Musical".
Singapore, which is 74 percent ethnic Chinese, 13 percent Malay and nine percent Indian, has strict laws on stirring communal tensions.
"A great start destroyed by a single racist act from host Sharon Au. Will we ever learn?" posted one Twitter user.