Registration can be done online at hse.ie or by phoning 1800 700 700 if the child has a health condition that puts them at higher risk or if they live with someone who at higher risk.
Director of public health for the National Immunisation Office, Dr Lucy Jessop, said the vaccine is first being opened today for this category.
All other children will be invited to register for a vaccine in January.
“Clinical trials showed that this vaccine was highly effective at preventing Covid-19 in children,” Dr Jessop said.
"All vaccines are tested before they are approved for use in Ireland by the European Medicines Agency.
“We know from listening to parents that they have questions and concerns about the Covid-19 vaccine – particularly parents whose child is not at higher risk. I would encourage parents to take time to read more about the vaccines.
"Parents should get their information from a trusted source, such as hse.ie or a medical professional when making the decision to vaccinate their child.”
To register online, parents need a mobile phone number, Eircode, email address and their child’s Personal Public Service (PPS) number.
Children who don’t have a PPSN can be vaccinated, their parents can register them on the phone with HSE Live.
Once a parent registers their child, they will receive a text message with details of their appointment.
The vaccines will be given in vaccination centres.
Yesterday, the Department of Health reported 6,735 new Covid-19 cases.
As of 8am yesterday, 461 coronavirus patients were hospitalised, of whom 91 were in intensive care.