The 52-year-old presenter was admitted to a hospital in Tooting yesterday (February 21) and underwent an operation on her thigh after being "stamped on" by the animal.
Kelly has since taken to Twitter to inform fans of her mishap.
"Thanks for your get well tweets. Basically I fell off the horse while attempting a jump for the first time," she explained. "Unfortunately the horse stamped on my thigh.
"As a result - deep wound and lots of blood. Was treated by fab paramedics in ambulance - then given an op under general anaesthetic at hospital."
Kelly added that she will be forced to miss several editions of breakfast show Lorraine while she recovers.
"Will be in for a couple of days and [it] will take around four weeks to heal but will be back at work before that!" she added. "A bit bruised and battered but fine...Huge thanks to everyone at the scene and the amazing NHS staff - and to you for thinking of me!"
Kelly had been training with Sarah Brown, wife of ex-prime minister Gordon Brown, for a modern pentathlon in aid of children's charity PiggyBankKids.
"Our thoughts are with Lorraine as she recuperates following her unfortunate accident," said Brown, who is president of the organisation.
"She's such a good friend of PiggyBankKids and we would like to thank her for the contribution she has made and wish her a speedy recovery," she added.
A spokesman for Chessington Equestrian Centre, where the accident took place, told The Daily Telegraph: "Lorraine was having a private lesson and was supervised at all times."
Occasional Daybreak presenter Helen Fospero fronted today's edition of Lorraine in her absence, assuring viewers at the start of the show that Kelly is "on the mend".