Many have posted angrily on social media that Suhana Khan doesn't deserve the cover because she hasn't achieved anything to warrant being there.
The prestigious Vogue cover is normally reserved for top models, actresses or singers at the peak of their careers.
Suhana Khan describes herself as "student, theatre lover, future star".
Her father is known as the King of Bollywood and many have complained nepotism is why she is on the cover.
The fashion shoot was styled by Anaita Shroff Adajania, Vogue's fashion director and long-time friend of Shah Rukh.
It is her first ever photo shoot and interview.
The magazine's Instagram post introduced her as the new girl on the block. It got more than 36,000 likes.
Suhana gave her own response to the negativity in her interview: "I keep telling myself that haters are going to hate, but I can't honestly say that I don't get upset by it.
"It's annoying, but I keep telling myself other people have bigger problems."
Shah Rukh unveiled the cover at the Vogue Beauty Awards. Speaking at the awards he said he hoped it would not be seen as entitlement.
"Things went well for me but kids are kids, children are children, and in this changing world sometimes you need the assistance of friends to give them a little more comfort and self belief and self worth so I want to thank Vogue for taking my little daughter and putting her on the cover.
"I hope it is not taken as entitled just because she happens to be Shah Rukh Khan's daughter... Thank you for putting her in a place where the responsibility that you've put on her by putting her on this cover is going to remove some of the entitlement she has because of she happens to be my daughter."
In the magazine he said that he wants to see his children work their way up to achieve their goals.
"We have friends who are very well-meaning and think of my kids as their own, and they're all happy and keen to launch her... But I keep insisting that I don't want them designed as stars, I want them to be launched when they are good enough actors."
In her interview Suhana reveals plans to continue with education and go to university before trying to make it as an actress and she said her parents made her think long and hard about taking up the offer of the cover.
"I was excited when my parents brought it up," she said.
"I wanted to say yes straight away, but they wanted me to think about it - this is a very public thing. They wanted me to gain confidence from the experience, not lose it."
The photographer on the shoot Errikos Andreou believes she is going to go far.
"She blew everyone away with how natural she was in front of the camera. It is so rarely I come across talent like this, because despite what most people may think this does require talent! This girl has a shinning way ahead of her and I'll be watching!"