The BBC newsreader received medical treatment after she “stripped” the muscle on her rib.
She tweeted a video of her lying on the floor laughing as she inhaled pain medication Entonox on Friday.
However, she has vowed to perform on Saturday’s live show, where she is set to dance the Argentine Tango with partner Aljaz Skorjanec.
In the video, Kate said: “The last time I did this was in childbirth which was really good, actually I’ve forgotten how good it was.
“I’ve somehow stripped the muscle in my rib on my best dance, on my best dance.”
She then pointed the camera at the medic treating her injury, who joked she was “sucking the life out of” the pain relief.
He added: “It’s Nitrogen and Oxygen which is used to relax the muscles, which is why Kate is on the floor at the moment and she’s constantly sucking on it like it’s a cigar.”
Kate then said: “I will be dancing tomorrow, if it’s the last thing I do.”
She also revealed that preparations for her performance were still going on around her, as she was having fake tan applied at the same time as undergoing treatment.
She said: “Welcome to the world of Strictly, this is me about to have Eloise do my fake tan because I am going to be dancing tomorrow!
“This is how we roll in showbusiness, I am going to be dancing!”
As Aljaz entered the room, Kate partner told him: “Hello baby, I’m just saying that the show is going on, because I’m having a fake tan for tomorrow because I am going to be dancing.”
Kate is not the only ‘Strictly’ star to have injured herself this week, as Stacey Dooley also ended up in hospital after suffering a bruised rib.
‘Strictly Come Dancing’ continues on Saturday at 7.05pm on BBC One.