Scientists and charities say the human papilloma virus (HPV) jab will protect them from head and neck cancers.
HPV is sexually transmitted and girls aged 12 and 13 receive the vaccine to protect them against cervical cancer.
The Welsh government said it is waiting for advice from the Joint Committee on Vaccination and Immunisation.
Charities including Tenovus Cancer Care and organisations such as BMA Cymru and Cardiff University's HPV research team will deliver a letter to the Welsh government on Monday calling for the vaccination to be rolled out.
They told BBC Radio Wales' Eye on Wales programme the number of head and neck cancer cases are increasing.
Dr Mererid Evans, consultant oncologist at Velindre Hospital in Cardiff, said: "I've seen a difference in demographics over the last ten years.
"These are younger people with families, and three-quarters of those affected are men. The average age is 55 and most are non-smokers."
Jon Antoniazzi, from Tenovus Cancer Care, added: "HPV causes 5% of the global cancer burden.
"What the Welsh government could be doing right now is taking a progressive step to stem the tide of these cancers, and show that it really takes the public health of its citizens seriously.
"We urge them to diverge from central thinking and vaccinate boys now."
In 2008, a vaccination programme was rolled out in schools and 85% of girls in Wales have been vaccinated.
The Welsh government said: "We will await the committee's recommendations and will consider the implications for Wales of any proposed changes to the HPV vaccination programme."

It includes plans to cut red tape, develop infrastructure and make it easier for companies to do business.
The launch comes on the eve of Mr Modi's first visit to the US as prime minister.
Manufacturing contributes only 15% to India's gross domestic product; authorities want to raise it to 25%.
Mr Modi's 'Make in India' campaign comes a day after India sent its homegrown mission to Mars.
The Mangalyaan robotic probe, one of the cheapest interplanetary missions ever, was successfully put into the orbit of Mars on Wednesday morning.
"Whenever I met [business] people for the last few years they would tell me - we want to shift out... It pained me that people of nation are forced to leave," Mr Modi said while unveiling the campaign in the capital, Delhi.
"We do not want any industrialist being forced to leave India. I can say that we have been able to bring about a change in last few months."
Mr Modi said India must "increase manufacturing and at the same time ensure that the benefits reach the youth of our nation".
A boost to manufacturing will create jobs, increase purchasing power and create a larger market for manufacturers, he added.
India has a huge pool of talented people, Mr Modi said, adding that it was because of this talent that India was able to send the indigenously-built Mangalyaan to the orbit of Mars.
Mr Modi won the recent general election, promising to revive India's slowing economy and in the three months to June, the country's economy grew by 5.7% , its fastest pace in two-and-a-half years.
Boys should receive a cancer vaccine - already given to young girls - to stop them developing strains of the disease, experts have said.
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Prime Minister Narendra Modi has launched an ambitious campaign which aims to turn the country into a global manufacturing hub.