One private hospital told the BBC that 90 people are on a waiting list after it ran out of supplies last week.
Hundreds of thousands of people have signed a national petition for the jab to be offered to all children
It follows a case in England where a mother shared pictures of her daughter dying in hospital from the illness.
Under national guidelines, the vaccine is only available to babies.
All babies in the UK are offered a potentially life-saving vaccine against meningitis B as part of a national immunisation programme.
However, there have been calls for the age limit to be extended to children and teenagers.
Private hospitals in Northern Ireland are reporting an increase in the number of inquiries from the public about getting the Meningitis B vaccine.