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The pro dancer was dating former Love Island contestant Higgins in the run-up to the current series of Strictly, but they appeared to have broken up when they both removed all photos of each other from Instagram.
Rumours began to circulate that Pernice had joined dating sites before the relationship was over, but he seems to have denied it in a social media post about the split.
He wrote: "Hey guys – I hope everybody had a great Monday. Going into another wonderful training week – thank you so much for your amazing messages and your support this weekend.
"I get to live my dream every single day because of you – so thank you, thank you, thank you. I wanted to say a couple of things…"
Pernice added: "Firstly, great relationships with great people can come to a natural end. This has been the case for me recently. There was absolutely no wrong-doing and this should be the end of any speculation.
"Whilst I respect and understand interest in my personal life, wouldn't it be fantastic to instead use this space to raise awareness of subjects and issues which need the attention."
In the current series of Strictly, Pernice is partnering EastEnders actor Rose Ayling-Ellis, the first deaf contestant to have taken part in the show.
Pernice continued: "My eyes have been opened to so many things during my career. But I am learning so much from this series of Strictly.
"The show has highlighted many important conversations for different communities and increased representation.
"These are the conversations which deserve the time, energy and recognition. We must concentrate on what's important and how we can all make a difference in life. Gio x."
Strictly 2021 also includes the show's first all-male couple, as former Bake Off winner John Whaite dances with Johannes Radebe.
The show's stars recently rallied around contestant Tilly Ramsay when she was targeted with cruel comments by radio host Steve Allen, who branded her "chubby" on air.
Watch: Who is Strictly's Rose Ayling-Ellis?