"Fan moment with @MadhuriDixit at @WomenintheWorld #delhi #witw," the filmmaker, who won the Oscar for her documentary 'Saving Face' in 2011, shared on Twitter.
She also posted an image in which she's seen posing with Bollywood's 'Dhak-dhak' girl.
Responding to the tweet, Madhuri wrote: "@sharmeenochinoy @WomenintheWorld It was a pleasure meeting you too! Wish you luck for the Oscar nomination."
They were both in the capital for the Women in the World summit, founded by internationally known journalist and author Tina Brown.
At the summit, Madhuri spoke about her life as an actress and humanitarian; while Obaid Chinoy was part of the event as moderator of a segment where two inspiring mothers shared stories of how they rose above personal catastrophe and forged a bond of reconciliation and peace.
The Pakistani filmmaker's next chance at an Oscar is courtesy 'A Girl in the River: The Price of Forgiveness', her new documentary that tells the story of an 18-year-old woman who survives an attempted honour killing.
The film is a semi-finalist in the 'Best Documentary - Short Subject' category.