The announcement by Robin Swann follows the latest advice from the Joint Committee on Vaccination and Immunisation (JCVI).
It also comes after Wales, Scotland and England also announced they would be following JCVI guidance.
The JCVI has advised that children in this age cohort are offered two 10 mcg doses of the Pfizer-BioNTech vaccine, with an interval of at least 12 weeks between doses.
The paediatric dose is a third of the strength of an adult dose.
In December, the JCVI had advised that children aged five to 11 years who were in a clinical risk group, or who were a household contact of someone who is immunosuppressed, should be offered vaccines.
Mr Swann said: "As has always been the case, our vaccination programme will continue to be guided by the expert advice.
"This announcement by the JCVI underlines the important role that the Covid-19 vaccines plays in protecting people of all ages and has only been taken after rigorous assessment of both safety and effectiveness.
"I have asked the PHA (Public Health Agency) to work with the (health) trusts to put this latest advice into operation and further details will be released shortly."
In a statement, the JCVI said: "This advice on the offer of vaccination to 5 to 11-year-olds who are not in a clinical risk group is considered by JCVI as a one-off pandemic response programme.
"As the Covid-19 pandemic moves further towards endemicity in the UK, JCVI will review whether, in the longer term, an offer of vaccination to this, and other paediatric age groups, continues to be advised."
The deaths of five more people who had previously tested positive for Covid-19 were reported in Northern Ireland on Wednesday, along with another 2,889 confirmed cases of the virus.
On Wednesday morning there were 474 Covid-19 patients in hospital, 12 of whom were in intensive care.