Sir Michael McBride was speaking as it was confirmed that the first case of the virus had been identified in the Province.
However, Sir Michael said he was confident that stringent public health measures would stop the disease from becoming endemic in the UK.
Health chiefs have also stressed that chances of infection remain low.
Northern Ireland was the last area of the UK to confirm a case of monkeypox on Thursday. No details of the infected patient have been released.
Speaking to the media, Sir Michael said it was not surprising monkeypox had reached Northern Ireland, given the number of cases reported in the rest of the UK.
He added: “The Public Health Agency is working closely with the UK Health Security Agency and partner organisations across these islands in terms of identifying possible cases, probable cases, or indeed any contacts.
“The key messages are that this is not an infection which is readily spread between people but can be by close contact.
“The risk to the general population is considered to be low.”
He added: “I can certainly say that I am fairly confident we will see further cases.
“I think that given the length of the incubation period and given the number of cases that we have seen across the United Kingdom, across Europe and globally, we will see more cases.
“What we want to do is to prevent this becoming established as an endemic infection in the United Kingdom because it isn’t at this time.
“We have a very good chance of doing that by taking all the steps we are currently doing.”
Dr Gillian Armstrong, head of health protection at Northern Ireland’s Public Health Agency, said that most people who contract monkeypox would recover within a few weeks.
She added: “It is spread through very close person-to-person contact, or contact with items used by a person who has monkeypox, such as bed linen.
“We have established a multidisciplinary incident management team here to ensure that we would be fully prepared for any potential or confirmed cases.
“We would like to urge anybody who thinks they might be at risk of exposure, particularly those who have developed an unusual rash or lesion on any part of their body, particularly the genital area, and especially those who have a recent new sexual partner, to limit their contact with others and to contact their GP.
“A notable proportion of the cases so far have been identified in gay, bisexual and other men who have sex with men. We are asking these people in particular to be aware of their symptoms.
“We will be conducting contact tracing to identify any of those who might be high-risk contacts to be advised to self-isolate or who might be eligible for a vaccination to prevent them going on to develop the monkeypox disease.”
She continued: “This is quite a rare condition, it is quite difficult to pass it on. This is not like Covid, it is much more difficult to transmit and we do have a range of measures to contain the spread of this.”
Dr Armstrong said that suspected and confirmed cases should self-isolate for 21 days.
Those with the closest contact to the case will be offered vaccination with the smallpox vaccine, to offer them protection.
Initial symptoms of monkeypox include fever, headache, muscle aches, backache, swollen lymph nodes, chills and exhaustion.
A rash can develop, often beginning on the face, then spreading to other parts of the body including the genitals.
The rash changes and goes through different stages – it can look like chickenpox or syphilis, before finally forming a scab which later falls off.