The reality star’s eldest child - who has Prader-Willi Syndrome, is partially blind and has autism - was admitted to Epsom Hospital on Sunday night with a high temperature and struggling to breathe.
A representative for Price confirmed Harvey, 18, has "undergone routine COVID-19 tests".
They added: "He's had the test because it's routine and not because they're worried that's what has caused him to go back into hospital and Katie remains calm. She is not panicking and her focus is on Harvey and his recovery. Harvey is trending all over the world and Katie is just now waiting on the doctor's advice."
Price, 42, wrote on Instagram: “I can confirm Harvey is in intensive care and in the best hands. I would like to thank the ambulance services and the hospital staff for the quick response and making him stable. X”
Kerry Katona has revealed she is looking after Princess while Harvey remains in hospital.
Katona shared pictures of herself and her own children enjoying a family day out at The Big Cat Sanctuary in Kent along with Princess.
In another post she shared a video of Princess lying in bed as she gave Instagram followers a tour of their holiday home. Princess admitted she was feeling tired after a “full-on day”.
Harvey - whose estranged father is the former footballer Dwight Yorke - was previously admitted to hospital at the end of June after he complained of chest pains that felt “like needles”.
Price is also mother to son Junior, 14, and daughter Princess with first husband Andre, as well as six-year-old Jett and five-year-old Bunny with third husband Kieran Hayler.