The BBC confirmed the news in a statement issued this afternoon (Thursday, 12 November).
They said that professional dancer Katya is asymptomatic and the pair are now self-isolating separately following the latest government guidelines.
"As part of the protocols outlined ahead of the series, this sadly means they will no longer be able to take part in the competition," the Strictly team announced.
Nicola said in a statement today: "Hey guys! I’m absolutely devastated my Strictly journey has come to an end so soon.
"I had so much more to give and so many people to win this for!
"But I just want to say a huge thank you to Katya for being the best dance partner anyone could ask for. She pushed me way out of my comfort zone and it’s been an incredible experience.
"I’m gutted to be out of the competition but in these unprecedented times and as frustrating as it is, the COVID measures in place are to keep everyone safe, and I’m doing what I can to help.
"I’ll be spending the next 14 days isolating so I’d like to apologise in advance for the ridiculous amount of TikToks I’ll be posting, in my new found free time when I’m not gaming!"
Katya added: “Dancing with Nicola has been an absolute inspiration. She's given her all each and every week and we were so excited to create more dances in the competition. Of course, I'm devastated to leave this way but I've made a friend for life and loved every moment of this special journey.
"I’d like to wish good luck to all the remaining couples!"
She went on to write on social media: "My heart is broken I’m utterly gutted this Special journey had to end this way and you don’t get to give more. @nicolaadams You are a woman who didn’t need a hero, you became one. Definitely my hero.
"To everyone, thank you for your tremendous support and we will keep dancing for you guys one way or another. #teamoutsidethebox @bbcstrictly.
"Meanwhile, please stay safe everybody. And to all my friends who’re still in the show- go for it!"
Olympic boxer Nicola and Katya had made history on Strictly as the first ever same-sex celebrity and professional dancer pairing.
Responding to the news, Strictly host Claudia Winkleman posted to Twitter: "We're so sad about this. Nicola and Katya were completely brilliant. X"
Added It Takes Two presenter Zoe Ball: "Gutted for Nicola and Katya. You made history girls. Sending them both all the love."
Sarah James, Strictly Come Dancing Executive Producer said in a statement: "We are incredibly sad that these unfortunate circumstances mean that Nicola and Katya are unable to continue on Strictly.
"They are a brilliant partnership and had already achieved so much during their time on the show.
"We'd like to thank them for their commitment and although their time in the competition has sadly come to an end we are hopeful that there will be opportunities for them to dance again in the future.”
The rest of the cast are unaffected and the show plans to continue as usual this weekend.
Strictly will air Saturday and Sunday night on BBC One.