The virus has broken out in the intensive care unit and renal department of St Helier Hospital in Sutton.
Ambulances are being diverted from A&E and visitors have been restricted, with the hospital in partial lockdown.
The coronavirus cases were discovered over the weekend and six patients are thought to be infected.
A hospital source said: “Infection control in intensive care is very strict.
“It’s very concerning that people fighting for their life already have become infected.”
An investigation into the outbreak has been launched.
A spokesman for Epsom and St Helier NHS Trust said: “A small number of patients have tested positive for COVID-19 during admission to the Renal Department and Intensive Care Unit at St Helier Hospital.
“The safety and wellbeing of our patients and staff is our priority and those who tested positive have been isolated from other patients, with arrangements in place to maintain safe and high-quality care.
“We continue to follow all relevant infection prevention and control guidelines.
“Visiting has been restricted for some areas, as soon as clinicians are confident that the measures can be lifted in a way that is safe for patients and staff, they will be.”
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