Published Wednesday, 01 July 2009
Michael McGimpsey said the majority of those who got the virus would only experience mild symptoms.
He said he was also confident the health service was prepared to deal with those whose condition became more serious.
"It`s a fine line between people being complacent and being over worried," he said.
"We have to find the middle way. Most people who get this will experience symptoms similar to seasonal flu, other more severe cases will will look to deal with those."
The minister gave the reassurances after a meeting with health ministers from across the UK at a meeting of the government's COBRA committee to discuss developments.
Vaccines
Mr McGimpsey said he had spent £55.3m on measures to contain and treat the virus, and warned that the total could rise further.
The first batch of vaccines are due to be available in September to coincide with the predicted surge of cases after the summer.
The minister said the policy of giving anti-virals to everyone who came into contact with infected people would not continue. They would now only be given to people who actually display symptoms in order to preserve stock levels, he added.
"We currently have very high rates of swine flu in Scotland and England and effectively this is where Northern Ireland will go," Mr McGimpsey said after the COBRA briefing.
"We have done very well to contain the virus so far. But the public also have a role to play when it comes to issues like personal hygiene to try and to limit the spread."
New case
The minister's comments come as the Department of Health, Social Services and Public Safety said that one more case of swine flu has been confirmed in Northern Ireland.
This brings the total number of cases here to 34.
The patient is a male who has been in contact with a recently confirmed case returning from Mexico, thought to be the six-year-old boy whose illness caused the closure of St Ronan's Primary School in Newry.
He is recovering at home and is on antivirals.
A further 35 potential cases are currently under investigation by the Department of Health.