Another user added: "I have no real gripe with the K family but Vogue used to be chic," while another said: "This is disappointing."
Similarly, celebrity hairstylist Marcus Francis commented on the photo of the cover, saying: "Such a sellout choice @Vogue. The choices made for this iconic magazine are not what it once stood for. Disappointment is an understatement."
Some users branded the publication's choice to feature the mother-of-three on the cover as "lazy", with one user saying they think there are other people that should have been chosen.
"Ugh, why. There are so many other interesting women to feature. This feels like a very lazy choice," the Instagram user wrote.
Similarly, another wrote: "Of all the women in the whole world?"
Another user added: "Very lazy choice @voguemagazine. Of all the interesting and inspiring women out there, this can't be the person you choose [to] celebrate.
"Such a bad message to young girls. American @vogue is soooo over. Anna Wintour needs to retire, this celebrity obsession is weird and old," they added.
One reader of the magazine said: "I'm so close to unsubscribing," and another added: "I know fashion and THIS IS NOT FASHION!"
However, despite a negative response to the cover, many have supported the magazine's choice to feature the Keeping Up With The Kardashians star.
One user said: "I liked it and I'm so sorry to all the models but I'm not sorry that Kimmy's on the cover.
"You get on the cover of Vogue, you earned it," they added.
Another user said: "Why is everyone hating on Kim like give her a break," while another said the cover was "well deserved" by the reality TV star.
"You're doing amazing sweetie," another added.
One excited reader said: "OMG!!! SOOO GOOOD!! I AM LIVING FOR IT", while another added: "Wow, haters everywhere. Did anyone even read the article? There's a reason behind why they've picked her for the Vogue cover. Anyways.. #judgementalpeople."
Kim since posted about her cover, revealing that she is grateful to have been chosen to feature in the iconic magazine, and that the experience has been a dream come true for her.
Posting several photos from her shoot, Kim said: "I've dreamed of this moment for so long, many said it would never come. Words cannot begin to express how much of an honor it is to have my first solo US cover of @voguemagazine. I remember as a little girl flipping through my mom's subscription each month and dreaming of one day gracing the cover of this iconic magazine.
"Thank you to the incredible Anna Wintour for your support as always, it means the world to me.
"@Tonnegood, @Mikaeljansson, and the glam team were an absolute dream to work with. I'm so incredibly grateful to writer @Jonathanvanmeter for illustrating a glimpse into my life in a way that I don't think has ever been done - from juggling family, my businesses and pursuing a law degree with such care and seriousness. Special thank you to my husband Kanye for speaking into existence that one day I would grace the cover of Vogue when everyone told me to be 'more realistic.'"
Kim previously appeared on the magazine's front cover with husband Kanye West, 41, in April, 2014.