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The former S Club 7 star was due to skate for the first time in Sunday's show but fell during rehearsals and is thought to have fractured her wrist.
However, she has now told fans she is doing whatever she can to get back on the ice and looks set to make her debut in week three of the ITV show.
“Thank you so much for all your lovely messages of support today,” the 43-year-old wrote on Instagram.
“A huge thank you to @sharonmorrisonuk and all the team @dancingonice for taking such good care of me.”
Stevens – who is paired with pro Brendyn Hatfield in the competition – went on: “My wrist is healing really well and @brendynhatfield and I have been working really hard and doing everything we can to get back on the ice as soon as possible.
"I’m so lucky to have such a great partner and we’re so excited to share our performance with you week 3!"
"Bring it on!” she added.
The star’s fans and celebrity friends have been wishing her a speedy recovery.
I’m A Celebrity’s Arlene Phillips wrote in the comments section: “I was so looking forward to seeing you. Take care. Come back strong darling.”
Skater Matt Evers posted: “Get well soon beauty…”
The singer’s former S Club bandmate Jo O’Meara posted a string of hearts.
Stevens is not the only person who has had to miss a show.
Happy Mondays star Bez has already announced he will not be able to attend this week's programme after testing positive for COVID-19.
Watch: Rachel Stevens pulls out of Dancing On Ice debut due to injury