This can occur if too much water is drunk over a short period of time.
Symptoms include nausea, vomiting and headaches. In serious cases, the brain can swell, which can lead to confusion, seizures, coma and death.
A death rate of almost 30 per cent has been reported in patients with abnormally low salt levels.
Writing in the journal BMJ Case Reports, doctors said there was little evidence to know how much water is too much.
They described how their patient got worse after she arrived in hospital, writing:
"During her visit to the emergency department, she became progressively shaky and muddled. She vomited several times, was tremulous and exhibited significant speech difficulties."
Doctors were able to save the woman's life with treatment including restricting her fluid intake to a litre over the next 24 hours, but they said on another occasion a young woman suffering from gastroenteritis died after consuming too much water.
The patient, writing of her own experience in the same journal, said: "I lost 24 hours of my life when a simple UTI, or rather my actions in response to it, took over my life.
"I remember seeing my hand in front of me shaking rather violently and I wondered why I could not stop it, then realised that my whole body was shaking."
She spent 24 hours in hospital - long stretches of which she cannot remember - before she was discharged.
"It took about a week to feel 'normal' again and if I am honest I think I was tired for at least another week," she wrote.
People who take the drug MDMA and those taking part in endurance sports are also at risk of very low salt levels.
The doctors - Dr Laura Christine Lee and Dr Maryann Noronha - wrote: "We frequently advise our patients to 'drink plenty of fluids' and 'keep well-hydrated' when they are unwell.
"But, what do we mean by that? Are there potential risks of this apparently harmless advice?
"As demonstrated here, the harmful effects of increased fluid intake include confusion, vomiting and speech disturbance, and potential for catastrophic outcomes due to low blood sodium concentrations."
They concluded: "There is a paucity of evidence behind the advice to 'drink plenty of fluids' in the management of mild infective illness."
But Dr Imran Rafi, chairman of clinical innovation and research at the Royal College of GPs, said: "Drinking enough water is important in keeping healthy, both physically and mentally, and patients should keep their fluids up when unwell, particularly in conditions that can cause dehydration.
"We would encourage patients to drink more if they have symptoms of dehydration, such as feeling thirsty - including in hot weather or when exercising - or passing dark-coloured urine. There is no steadfast recommendation as to how much water people should drink in order to stay healthy, but the key thing is to keep hydrated - and passing clear urine is a good indication of this.
"This case report highlights that excessive water intake can have important consequences for patients, and this is something that healthcare professionals, and patients, should be mindful of."
