Posing for photographer Greg Swales, Kim spoke about growing up in her famous family, documenting her everyday life on camera, and building her business empire.
But one reader wrote: "Umm Kim K for Vogue India? Wearing a lehenga?"
Another reader blasted: "I can't believe @VogueIndia featured Kim Kardashian on their cover as if we don't see her featured on a different magazine every day.
"India's Vogue should embrace and feature their own south Asian women instead of choosing someone from pop culture."
One even accused the fashion bible of "perpetuating a detrimental cycle of underrepresentation", adding: "Stop whitewashing your own damn culture."
However not everyone was upset by the cover; The Quint praised the "stunning" images, writing: "Kim Kardashian in an Indian label - yes, it finally happened."
Others were quick to point out that Vogue India only feature international models "once in a blue moon" - with the majority of their cover stars being Indian.
Actresses Deepika Padukone and Kareena Kapoor were Kim's predecessors - with one notable exception being Kim's half-sister, Kendall Jenner, who also raised eyebrows when she graced its cover in May 2017.
In her Q&A with Vogue India this week, the reality television star admitted that she 'didn't actually' imagine her incredible empire growing to the size it is today.
"I thought I was just going to run my clothing store," Kim said. "I didn't think [the show] would go beyond Season 1 or 2. And then as things were happening, my mum and I were so excited."
"We didn't even know what we were starting, but we knew we were in it together," she added. "We definitely made so many mistakes. At first, we would be involved in anything.
"But it helped us work our way up to now, to launching a beauty brand completely by myself, and funding it all."
