Four out of 10 people believe getting treatment for a mental health issue is a sign of personal failure.
A study found 60% of the public would discriminate against hiring someone with a history of mental illness on the grounds that they may be unreliable.
Elsewhere, more than a fifth believe those suffering are of below average intelligence, while 30% would not willingly accept someone with depression, anxiety or another illness as a close friend.
Some 500 members of the public were questioned for the St Patrick's Mental Health Services survey to mark World Suicide Awareness Day.
Paul Gilligan, St Patrick's chief executive, said society needs to challenge the stigma that exists around the issue.
"Each year we continue to be disturbed by the level of stigma that still exists towards those with a mental health difficulty," he said.
"We know that one in four of us will have to deal with such a difficulty like this at some point in our lives. That means every single family in Ireland is affected by mental illness.
"We need to challenge the stigma that exists and prioritise mental health in the same way we do our physical health."
St Patrick's said a lack of understanding of mental health problems is still fuelling stigma and preventing people from accessing support.
Its survey revealed that 41% of people felt that undergoing treatment for a mental health problem is a sign of personal failure.
However, more than half of those quizzed had a close friend who had been treated for emotional or mental health problems, 49% worked with someone who had, and 37% of respondents revealed close member of their family - like a parent, child, brother, sister - had got help.
"It has been said that physical health is easier to understand because we know that healing is possible," said Mr Gilligan.
"However, there is a need to promote mental health education in Irish schools and workplaces to ensure that everyone knows that recovery is possible and those that need help don't wait to get that help."