Vaccines for those aged 12 to 15 should be finished by early October, according to the HSE.
COVID-19 vaccine registration is now open for 12 to 15-year-olds - parents can sign them up online or by phone.
An adult must accompany the child to the vaccination centre, pharmacy or GP.
Dr Lucy Jessop is director of public health at the HSE's National Immunisation Office.
She told Newstalk Breakfast she is hopeful the programme will be completed within two months.
"If people start being vaccinated from this weekend, it really would depend on how fast people are registering on the portal.
"Obviously it's summer holiday time, people may not be in Ireland at the moment, they may be away.
"So it may take a few weeks to get through the first dose... the second dose is three weeks later - so that would probably be around the time that they're going back to school.
"I would hope most of the second doses would be finished by early October".
Dr Jessop says vaccines should start by this weekend, or possibly even earlier.
"Appointments will be issued quite quickly after people have registered on the line.
"We're hoping vaccines will start this weekend, possibly even a little earlier.
"I think pharmacies and GPs may even be offering it a little earlier now."
She says the majority of children will be called out to one of the large vaccination centres.
But that some pharmacies and GPs are also offering vaccines.
"There are also pharmacies offering the Pfizer vaccine, and a list of those are on our HSE website.
"So if that's more convenient for parents they can look for a local pharmacy and some GPs are also still offering the vaccine as well".