The gene controls the development of hormone-regulating neurons that tell the body when to reach sexual maturity.
Researchers from Queen Mary University of London identified the fault by studying cases of delayed puberty within seven families.
The finding, reported at the Society for Endocrinology annual conference, may point to a new way of treating the condition.
Girls normally show signs of puberty before they reach 13, and boys by 14 or 15.
If a teenager older than this is not showing any such signs – breast development in girls and growth in testicle size in boys – then this should trigger alarm bells with their doctor.
Four in every 100 adolescents experience early or late puberty.
The GnRH gene error may account for many of such cases, Dr Sasha Howard and colleagues told the Society for Endocrinology annual conference.
Their work looked at seven families from Finland, but they say the findings are applicable to the UK and other Western European countries.
By scanning DNA samples, they identified 15 candidate faulty genes, but one stood out.
This, as yet, unnamed gene error interrupts the development of gonadotrophin-releasing hormone (GnRH) neurons in the brain of the foetus in the womb.
And puberty is affected by varying degrees, according to the severity of the gene error.
A small gene error could delay puberty by a couple of years, for example, while a larger error might block puberty altogether.
Dr Howard said: “This is useful to know and could ultimately lead to better treatments and diagnostic tests.
“If we had a gene panel that we could test we could reassure some patients that they will go into puberty eventually.”
She said the search was on for other genes that influence puberty onset.
“There’s a small handful of genes that have been implicated in early or late puberty so far. There will undoubtedly be more.
“Our discovery is exciting though because it reveals a novel mechanism that we didn’t know about before.”
Prof Richard Sharpe, an endocrinology expert at the University of Edinburgh, said: “Delayed puberty can be extremely embarrassing and distressing and, in some cases, can have health consequences, such as bone problems from prolonged growth.”
Knowledge such as this could help doctors better judge which patients need treatment to help them reach puberty, he added.