Claudia, 42, has had to pull out of the show for the third week running as she is caring for her seriously ill eight-year-old daughter Matilda.
Matilda is currently in hospital with severe leg burns, after her black wizard Halloween costume was accidentally set on fire by a candle while she was out trick-or-treating with friends.
A witness said that Matilda's outfit turned into a 'crackling ball of flame' and melted onto her skin before she was rescued by a passerby - Jamie Poulton, 45, who plucked her from the group of screaming children and extinguished the fire with his hands.
Claudia and her family issued a statement at the time of Matilda's injury thanking everyone for their support, in particular the NHS doctors, nurses and staff whom they described as 'incredible'.
It continued: "We would like to take this opportunity to remind anyone taking part in fireworks parties or Guy Fawkes celebrations to be vigilant about the dangers of candles, open fires and fireworks and to be please have the appropriate safety measures in place and to hand."
Claudia became Tess Daly's co-presenter on Strictly when Sir Bruce Forsyth, 86, retired ahead of this series.
"Getting the gig on Strictly was a dream for Claudia, so it's cruel that she has had to pull out when things were all going so well," a source told The Sun.
"But she is not going to leave Matilda's side until she is sure she is ready.
"Matilda is taking great strides in her recovery, but is a long way off being completely better and Claudia just doesn't think it would be appropriate to be on stage being upbeat while her daughter is unwell.
"At this stage she is refusing to put a time on when she'll be back. She is going to give it as long as it takes and the BBC is being incredibly understanding."
Claudia and her husband, film producer Kris Thykier, 42, have two other children - Jake 11 and Arthur, three.
Claudia's absence is being covered by It Takes Two host Zoe Ball, who will be joining Tess Daly at the Blackpool ballroom this Saturday (November 15).
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