"We apologise for causing concern and anxiety among people due to... Our initial judgement on the contagiousness of MERS," Minister Moon Hyung-Pyo told reporters.
Moon added this week would be a "critical period" to contain the spread of MERS, or Middle East Respiratory Syndrome, which can cause symptoms ranging from flu-like aches and pains to pneumonia and kidney failure.
"We are making our utmost efforts to prevent the further spread of the disease," Moon said, urging the public not to panic.
The 44-year-old left on a business trip on Tuesday, a day after his father was diagnosed with the virus, and was confirmed Friday to have been infected himself.
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The man flew to Hong Kong before travelling by bus to the Chinese city of Huizhou, where he is currently being treated under quarantine.
Dozens of people -- including his colleagues and passengers who sat near him on the same flight -- have been or are expected to be examined or quarantined.
The current outbreak has meanwhile been traced to a 68-year-old man diagnosed on May 20 after returning from a trip to Saudi Arabia.
Moon said the hospital where the first outbreak was reported has been closed and all patients were being treated in quarantine, but would not disclose its name or location for fear of spreading panic.
MERS is considered a deadlier but less infectious cousin of Severe Acute Respiratory Syndrome (SARS), which killed hundreds of people when it appeared in Asia in 2003.
A total of 129 people who were exposed directly or indirectly to the patients have been quarantined or put under special observation so far.
More than 20 countries have been affected by the virus with no known cure or vaccine, with most cases in Saudi Arabia where more than 400 have been killed since 2012.
The South's outbreak of MERS is the largest among countries outside the Middle East.