Smriti had attended a six-day leadership programme along with 11 other Indian MPs last year and got a certificate for it.
Irani had allegedly made the remark when one of the members of the audience asked her about her education qualification at the India Today Woman Summit 2014.
At the event on Saturday Irani was allegedly quoted as saying: "In that kitty of mine where people call me 'anpad' (illiterate) I do have a degree from Yale University as well which I can bring out and show how Yale celebrated by leadership capacities. Extraneous circumstances are being created so that I deviate my concentration from what my goals are. I should be judged from what I deliver as a minister."
Soon after the Lok Sabha results were announced on May 16, Irani was at the centre of a controversy over her educational qualifications after it emerged that she had made contradictory declarations when she contested the parliamentary elections in 2004 and 2014.