The analysis was carried out by the Epinion institute on behalf of trade union LO and reported by newspaper Politiken on Monday.
In the survey, 5,819 people were asked how often they take medicine to help with their metal well-being. 14 percent answered that they take medication daily or weekly.
The survey also asked 3,360 people, who were either in employment, on sick leave or receiving unemployment welfare payments, whether they had taken sick leave from work during the last 12 months due to stress, burn-out or similar complaints.
Of those, 18 percent responded that they had taken sick leave due to stress-related symptoms.
The statistics take into account both academics and unskilled workers, writes Politiken.
"This is a very serious issue, with so many working people required to take medicine to be able to cope with the mental demands of their jobs," LO deputy chairperson Morten Skov Christiansen told Politiken.
"It shows with a concerning clarity that more focus needs to be placed on the psychological aspects of working environments," Christiansen said.
The LO deputy chair pointed to the fact that 98 percent of orders given to businesses --requiring them to improve workplace conditions - by the Danish Working Environment Authority (Arbejdstilsynet) relate to physical, rather than psychological issues with the workplaces.
The study did not look further into the type of medicine respondents were taking, Politiken reports.
But the one-in-ten figure for working people taking medicine for stress is unsurprising, according to Michael Dupont, deputy chairperson with the Danish Medical Association.
"We have found that a lot of people have hard working lives and are battling to make things fit together. That is particularly the case for parents of young children, who experience pressure both at work and in their private lives, where they have a lot to do," Dupont told Politiken.
"And you cannot then rule out feeling that you need to take some form of medicine," added Dupont, who is a GP.
The Danish Medical Association vice chair added that doctors do not prescribe medicine for stress unless it is part of a set course of treatment.
Katrine Marie Jensen, a stress consultant and advisor to businesses and individuals, said the findings of the analysis were "alarming".
"It is alarming that people feel they need medicine to be able to go to work. It is predicted that stress will be the primary cause of sickness [causing absence from work, ed.] in 2020. It is very worrying that we as a society are heading in that direction," Jensen said to Avisen.dk.
Managers and employees must work together to find a solution to the increasing problem, she added.
"The greatest responsibility lies with management. They must get involved, talk about what stress is, and find out how to prevent it," she said.
"But there is also a shared responsibility. If you can see your colleague is not feeling great, you should say something to him or her and help," she added.