Mr Hwang said that as there had been no new infections for 23 days, the public could be "can now be free from worry".
He also apologised for the government's much-criticised response to the virus, which has killed 36 people in South Korea, Yonhap news agency reports.
But the WHO said it was not yet declaring Mers officially over.
Middle East Respiratory Syndrome (Mers)
Mers is caused by a coronavirus, a type of virus which includes the common cold and Sars (severe acute respiratory syndrome).
First cases emerged in the Middle East in 2012, and the first death in Saudi Arabia in June that year.
Believed to have originated in camels, though the transmission to humans is not fully understood.
The virus does not pass easily between humans - infections usually occur in people who have had close contact with an infected person.
Patients have a fever, cough and breathing difficulties, but Mers can also cause pneumonia and kidney failure.
Approximately 36% of reported patients with Mers have died - there is no vaccine or specific treatment.
A spokeswoman in Manila said the WHO required 28 days without a new infection to make the announcement - twice the virus's incubation period. The last case was confirmed in South Korea on 4 July.
'Shake off all concerns'
Speaking in Seoul Mr Hwang said that "after weighing various circumstances, the medical personnel and the government judge that the people can now be free from worry".
"I ask the public to shake off all concerns over Mers and to resume normal daily activities, including economic, cultural, leisure and school activities," the Yonhap news agency quoted him as saying.
"I am sorry to the people for causing worries and discomfort."
Mers appeared in South Korea on 26 May, brought by a man who had visited the Middle East, where the disease was first identified in 2012.
South Korea - the only outbreak outside the Middle East - has confirmed 186 infections, with 36 deathss.
The government was accused of being slow to react to the crisis, with most of the infections happened at health centres which were not adequately prepared for a contagious disease.
The outbreak - and subsequent quarantining and restrictions on daily life - have had a disastrous effect on the economy, with tourism seeing a 40% drop in foreign visitors.
Last week, the government approved a 11.5-trillion won ($9.84bn; £6.3bn) package to help the struggling economy.
