Miss Khan, who is holidaying on the Croatian island of Hvar with her family, subsequently alerted the police to the threat.
Sharing a screenshot of the message on Twitter, she wrote: ‘Just received a death threat from a @silverbengle on Instagram – check it out @metpoliceuk’.
On Tuesday night, a spokesperson for the Metropolitan Police said: ‘The Met’s digital contact team @MetCC have messaged a 47-year-old woman with a view to formally reporting an allegation of malicious communications. Enquiries continue.’
The news comes after the latest guidance from the Crown Prosecution Service warned that people face prosecution for hate-filled online messages in the same way as if they abused people in the street.
Miss Khan’s bikini post was made in response to a video sermon that emerged this week of burqa-wearing Australian Muslim preacher Umm Jamaal ud-Din saying it was sinful for women to pluck their eyebrows and uploaded to her YouTube account on Monday.
The subsequent bikini post from Miss Khan was swiftly ‘liked’ by more than 800 of her followers, many of whom supported her following the threat.
One wrote: ‘Saira you are an amazing, inspirational and beautiful lady.’ Another added: ‘Best response ever! I wish more Muslim women would response to misogyny openly!’
Last year, Miss Khan made headlines when she admitted that her sex drive had become so low she had given her husband, Steven Hyde, permission to have an affair.
The former Apprentice runner-up told ITV’s Loose Women: "I’m 46, I have a busy life and two kids. I am so lucky. We used to have a fantastic sex life."
"I still love my husband, we cuddle and it’s lovely. But I’m not interested [in sex]. I don’t want to. I’ve lost the desire and I find myself making excuses from around 6pm."