Tedros Adhanom Ghebreyesus on Friday urged countries to supply more vaccines to the global fair-access scheme Covax.
The international distribution of Covid vaccines remains vastly uneven.
Since the first vaccines were approved in December, wealthier countries have bought up most of the supply.
Many are racing to vaccinate as much of their population as possible.
Speaking at a virtual conference in Geneva on Friday, the WHO's Dr Tedros said he understood why some countries wanted to vaccinate children and adolescents, but said "right now, I urge them to reconsider".
"In low and lower-middle income countries, Covid-19 vaccine supply has not been enough to even immunise healthcare workers, and hospitals are being inundated with people that need lifesaving care urgently," he said.
Last week, US President Joe Biden laid out plans to begin coronavirus vaccine shots for 12- to 15-year-olds as soon as possible. He also said he hoped that 70% of US adults would receive at least one dose of a Covid-19 vaccine by 4 July, when American families are expected to come together to mark Independence Day.
Meanwhile, Canada has authorised the use of the Pfizer coronavirus vaccine for children aged between 12 and 15. The province of Alberta, which has the highest rate of the virus in the country, has already started offering the jabs to citizens over the age of 12.
In Switzerland, some places began offering Covid vaccination appointments to 16-year-olds last week.
So far, the US and China have administered the highest number of vaccine doses overall, with India in third place. But while nearly all of Europe and the Americas have begun vaccination campaigns, a few countries in Africa are still to get started.
The Covax scheme was developed with the aim of first vaccinating 20% of the population in the 92 poorer countries that signed up, starting with health workers.
The scheme is co-led by the WHO, the Global Vaccine Alliance (Gavi) and the Coalition for Epidemic Preparedness Innovations (Cepi), with the UN children's fund, Unicef, as key implementation partner.
During Friday's conference, Dr Tedros also warned that the second year of the pandemic was likely to be deadlier than the first, and that the situation in India was of grave concern.
In India, many health workers on the frontline dealing with coronavirus patients have not been vaccinated, and some are dying. The severe shortage of doses comes amid a deadly second Covid wave and warnings of an impending third wave.