The TV presenter was noticeably absent during this weekend's Strictly Come Dancing live shows, as she was by her eight-year-old child's side after the accident.
A statement issued on the behalf of Claudia and husband Kris Thykier said: "Our daughter was involved in an accident on Friday night while celebrating Halloween. She is having the best care possible and we are hopeful of a full recovery.
"We would like to thank everyone that has been so supportive and particularly the NHS doctors, nurses and staff who have been absolutely incredible."
The nature of Matilda's injury has not been revealed.
Today's statement 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 presents Strictly alongside Tess Daly but last weekend viewers saw Zoe Ball stepping in as her replacement.
They were told that one of Claudia's children was unwell but the nature of the illness was not disclosed.
Claudia and husband Kris are also parents to two other children.