The 43-year-old reality star and mother-of-five – who was serving a driving ban – crashed her car in the early hours of Tuesday And was taken to hospital for treatment following her arrest.
Woods posted a statement on social media saying: "Relationships are tested, people test each other – but when you love someone like I love Katie, you enjoy the highs and good times together, and that bond is tested during the low and difficult times together.
"Katie is a tough diamond. She has her imperfections however they make her just perfect to me, she just needs that extra help to be polished.
"The sunshine will shine through her once against and the sparkles that she brings to everyone will return.
"I love you Katie 100%. My Dolly. Always here, always will be."
Price's family voiced concern for her mental health in a statement on her official Instagram account.
Her daughter 14-year-old Princess commented on the post: "Love you mum so much."
The statement read: "This message has been written by Kate's family.
"As a family we have for some time been concerned about Kate's wellbeing and overall mental health. Today our worst fears nearly came true.
"As a family we have been and will continue to help Kate get the help she needs.
"We hope that she will realise that she cannot battle her issues alone. We would kindly ask that the media and wider public give Kate the time and space she needs to seek the necessary treatment, so that she can hopefully return to the Kate we know and love as a mother, daughter and sister.
"We are concerned and worried about her deeply, we know she lives her life publicly and to many she is fair game, but as a family we hope she can find her path privately moving forward during this very difficult period in her life.
"We are not asking for sympathy – just that it is recognised that Kate is unwell.
"We take great comfort in reading the messages of support and love for Kate that we will pass on to her, in the hope that these positive messages will help spur her on.
"It takes great strength for one to acknowledge they need help, we hope the door is now open for Kate to learn to love herself and to be happy within. Mental illness is not a personal failure.
"The Price Family xxx"
A Sussex Police spokeswoman told The Mirror: "Police responded to reports of a single-vehicle collision around 6.20am on Tuesday.
"A woman, 43, was arrested on suspicion of driving while above the legal limit for alcohol and drugs, and has been taken to hospital to be checked over."
The former glamour model – who was declared bankrupt in 2019 – is mother to 19-year-old son Harvey, whose father is footballer Dwight Yorke; teenagers Junior, 16, and Princess, 14, with first husband Peter Andre; and Jett, eight, and Bunny, seven, with third husband Kieran Hayler.
Price – who has previously spoken about her treatment for cocaine addiction – returned to rehab at The Priory clinic at the beginning of 2020.
Katie began dating 32-year-old car dealer Carl Woods in June 2020 and in April this year they announced they were engaged to be married – her seventh engagement.
Last month Essex Police confirmed that an unnamed man had been arrested on suspicion of assault, theft and controlling behaviour following an alleged attack on Price in the early hours at her home.
Watch: Katie Price on GMB one day before her arrest