The ministry also said another patient infected with the MERS virus had died, taking the death toll to 16 since the outbreak began in May.
Up to 17 patients are in an unstable condition.
The five new patients — aged from 39 to 84 — were infected in hospitals in cities including Seoul and Daejeon, 140 kilometres south of the capital.
Among them was a doctor who had performed CPR on an infected patient in Daejeon and one infected in Samsung Medical Centre in Seoul — where more than 70 patients, visitors and medical staff have contracted the virus.
On Sunday, the Samsung Medical Centre suspended its services after being identified as the epicentre of the spread of the deadly infection.
Among the cases was an emergency ward orderly who worked for days after developing symptoms, coming into contact with more than 200 people, the hospital said.
Authorities have also sealed off at least two other hospitals with patients and medical workers inside.
The number of people who have come into contact with patients and put under quarantine either at state facilities or at home has risen to 5,200.
The outbreak started on May 20 when a 68-year-old man was diagnosed after returning from a trip to Saudi Arabia.
Since then the virus has spread at an unusually rapid pace, sparking alarm in Asia’s fourth-largest economy. Almost all patients were infected in hospital.
Most of those who have died from the disease have been elderly people, or people with existing ailments.
The World Health Organisation has called an emergency meeting for Tuesday on South Korea’s “large and complex” MERS outbreak.
MERS is caused by a coronavirus from the same family as the one that caused SARS. There is no cure or vaccine.
Reuters