The reality star claimed she was never made aware that the international cover shoot would end up on the Turkish version of the magazine, insisting that she would never have agreed to the shoot if she had known.
Genocide Remembrance Day marks the extermination of the Armenian population by Turkey during and following World War I.
Speaking on her blog, the Kourtney and Kim Take New York star wrote: 'I had no idea that Turkey was planning to run my story on their cover THIS month, considering Genocide Remembrance Day is this month.
'My Armenian heritage means a lot to me and I have been brought up to be incredibly proud of my family's background and culture so as an Armenian-American woman it is a huge honour for me to be on the first ever Armenian Cosmopolitan cover.'
On April 24, the Armenians will commemorate those lost in the genocide, just weeks after the 30-year-old appeared on the front of the magazine in Turkey.