The former Hollyoaks star, 28, said she feels like she has been "run over".
She shared a series of videos on Instagram which showed her in a hospital bed with an oxygen mask on.
Davis told fans she was "in so much pain" and that her skin felt sore.
"Hello guys, so last night I got a bit of a headache before bed and my sinuses, I woke up and I felt so ill, I had to call an ambulance basically," she said.
"I've tested positive for COVID.
"I feel like I've been run over. The worst part is that my skin, my front and back of my skin, I can't touch my skin, it's killing me."
She went on: "I'm just in so much pain, oh my God it’s horrible. It happened so quick, I don't even know... I just woke up and I couldn't move.
"Obviously I've never had sore skin before so I thought this isn't a chest infection or what I would normally suffer with my chest. I feel rotten."
Another video showed the actor with the oxygen mask off and a normal facemask on.
She told her fans she was in and out of sleep and that she had been started on fluids and intravenous painkillers.
“Honestly, my God. I feel like I've been ran over," she said.
Davis played Sinead O’Connor on Channel 4’s Hollyoaks on and off for 10 years.
Watch: Caroline Flack 'wasn't treated like a human'