Health officials are now trying to trace where she contracted the virus and who she has been in contact with, she added.
Six people have died in Britain from the virus, with more than 370 confirmed cases.
Dorries, who helped craft the legislation to fight the bug, is the first British politician to be diagnosed with COVID-19.
The Times reported that she had been in touch with hundreds of people, including Prime Minister Boris Johnson.
She fell unwell on Friday while signing the document that declared coronavirus a notifiable disease, meaning companies could obtain insurance cover, said the paper, adding she was now believed to be on the road to recovery.
“I would like to thank… the wonderful NHS staff who have provided me with advice and support,” she said, referring to Britain’s National Health Service.
The shock news is likely to increase calls to suspend parliament, despite the government’s reluctance to do so in the middle of a health crisis.
Her boss Matt Hancock, who is leading Britain’s response, tweeted that he was “sorry to hear Nadine has tested positive for coronavirus.
She has done the right thing by self isolating at home, and both NHS and PHE staff have been brilliant. We all wish her well as she recovers,” he added. PHE refers to Public Health England