Almost half of 2,215 16- to 25-year-olds polled by YouGov for the Prince's Trust said they had themselves experienced a mental health problem.
And a third of these felt admitting to problems could harm their job chances.
Fear of stigma was a "major obstacle" to finding help, said Prof Louise Arseneault, of Kings College London.
A third of the young people sampled also said they would worry about appearing weak if they sought help, and most said they would not want to confide in anyone at all.
Prof Arseneault, a mental health leadership fellow at the Institute of Psychiatry, Psychology and Neuroscience at Kings College, said it was "extremely worrying to see that young people suffer from the stigma around mental health".
"This can be a major obstacle for them in seeking help and finding support, which could further affect their confidence in finding work at a crucial stage in their lives.
"It shouldn't be like this.
"Increasing the understanding and awareness of mental health problems among young people should be a key priority.
"We also need to explore ways of ensuring young people with mental health problems do not fall out of education or employment at an early age."
The findings are the second instalment of anonymised research carried out online in November among a representative sample of young people from across the UK for the Prince's Trust Macquarie Youth Index.
The first instalment was published in January.
Over three-quarters of young people say there is a stigma to mental illness and a quarter would not ask for help if they were suffering, a survey suggests.