Irani posted on Twitter a few pictures from their meeting.
"In conversation with @anitadongre for taking forward #IWearHandloom to support our weavers," the minister tweeted.
Irani has been promoting handlooms on social media since she took charge of the textile ministry.
On Monday, Irani tweeted a photo of herself in a blue silk sari, captioning it, "I support Indian weavers, here's my #IWearHandloom look - handwoven silk from Bihar."
She further explained how the campaign worked. "Share your look and tag five people," she wrote.
Among them were sports personalities like Vijender Chauhan and Virender Sehwag; designers like Manish Malhotra and Suketu Dhir; while the political sphere was represented by Jaya Jaitly and Amruta Fadnavis.
Irani's "Selfie With Handloom" campaign, will go on till August 7, which is observed as National Handloom Day.