The poll, commissioned by the Mental Health Foundation, also found more than a third of people (35 per cent ) had experienced suicidal thoughts or feelings because of stress.
One sixth of people (16 per cent ), meanwhile, said they had self-harmed as a result of feelings of stress.
The study was commissioned by YouGov as Mental Health Awareness week was launched, which has been run by the Mental Health Foundation for the past 18 years.
The study, which quizzed 1,012 people, is included in a new report by the Mental Health Foundation published on Monday called Stress - Are We Coping?
Lee Knifton, head of Mental Health Foundation Scotland, said: “Very large numbers of adults in Scotland are experiencing high levels of stress and it is damaging our health.
“Stress is one of the great public health challenges of our time, but it still isn’t being taken as seriously as physical health concerns.
“Stress is a significant factor in mental health problems including anxiety and depression.
“It is also linked to physical health problems like heart disease, problems with our immune system, insomnia and digestive problems.”
Ms Knifton said employers also needed to treat stress and mental health problems as seriously as physical safety.
She added: “We are also asking for well-being days to be provided to public sector workers as part of reducing the pressure on those who work hardest to look after us.”
A separate report by insurance firm Aviva also found day-to-day issues such as money worries, family and work pressures mean more of us “struggle to cope” at some stage.
The Aviva Wellbeing report questioned 4,205 UK adults, two thirds of whom suffered from stress (67 per cent ) and a similar number (64 per cent ) had depression.
Dr Subashini M, associate medical director at Aviva, said: “Our mental health is as important as our physical health, however too many people find themselves suffering in silence, with nowhere to turn for support or feeling as though they can’t discuss how they feel.
“Nearly half of us have been, or will be, affected by mental health conditions at some point in our lives, yet for the most part, there is still a distinct taboo in many circles.
“A persistent pattern of not directly acknowledging and addressing our own - and the UK’s - mental health issues only further reinforces stereotypes and taboos.
“Currently, half of adults in the UK state say they would feel uncomfortable discussing mental health - a mindset that in many cases can actually lead to greater suffering and isolation for those in need who become even more reluctant to speak to anyone.”