Khanjani has revealed she has been in isolation for more than a week, and her symptoms include fevers, coughing and loss of taste.
She believes she contracted the virus on Boxing Day when she visited a packed supermarket in the UK.
She updated her Instagram followers to let them know she's had the virus for over a week and is "over it".
Khanjani told Stuff she and her boyfriend visited the grocery store, which was packed with hundreds of shoppers.
The couple, who had been in a long distance relationship since May 2019, now live together in Milton Keynes, north of London.
"The next day I woke up coughing. I didn't think anything of it. Jonny started coughing on the 29th and we both started having fever-like symptoms," she told Stuff.
"He actually lost his sense of taste on the 31st and that's when we knew we had to book in to get tested in which we did on the 1st January. The test came back 3rd January as positive."
"Our bodies ached a lot towards the beginning but it only lasted for a few days," she added.
UK PM Boris Johnson has revealed that one in 50 people in England are infected with Covid-19 as he promises to keep the country updated "jab by jab" on his mission to vaccinate the most vulnerable by mid next month.
England is to remain in lockdown until at least March, and some measures could stay in place for even longer, as hospitals struggle to cope with the highly contagious new strain of the coronavirus.