A survey from insurance provider Friends Life has found that two in five adults have suffered from stress, anxiety or depression in the past year and have not told their boss.
Of those, a quarter said they had taken a sick day because of a mental health issue but lied that it was for a physical problem.
The most common cause of stress was excessive workload, followed by frustration linked to poor management and long working hours.
Jonathan Clark, director of Premier Mind and Soul, the community unit at Premier Christian Media, told the News Hour that too many people see mental health as a weakness.
He said: "If you start saying to your employers that you're finding it difficult to actually cope with the job – that you're under too much pressure, too much stress – they'll start to look at you and think: are they up to doing it?"
Andy Briggs, group chief executive of Friends Life, said: "These statistics paint a worrying picture of a culture of silence when it comes to mental health.
"Our research shows that there is still much to be done in tackling mental health issues in the workplace. Anxiety, stress and depression can affect anybody and employees need help and support so that they are not left feeling vulnerable and demotivated."
Hear more from Jonathan Clark, Premier Mind and Soul: