The survey by the charity Young Women's Trust revealed that just 6% of young women who have been sexually harassed at work say they have reported it.
This is despite TUC research showing that 63% of young women have experienced sexual harassment in the workplace.
When asked what would put them off reporting such behaviour, one in five said they feared being given fewer hours at work and one in three said they do not know how to report sexual harassment.
Anxieties around being fired for reporting sexual harassment were found to be higher among young women of colour, or with a disability or long-term health condition -- with 30% and 37% respectively saying they were scared this would happen.
Eight in ten respondents said they had been treated less positively by their employers because they rebuffed unwanted sexual advances, while 5% said they had had to leave their workplace for another job due to sexual harassment, assault or abuse.
Sophie Walker, chief executive of the Young Women's Trust, said: "We are calling on the government to make it mandatory for all employers to protect their workers and volunteers from harassment and victimisation.
"No woman should feel unsafe at work or put up with sexual harassment as something that's part of the day job - we've heard so many testimonies, read so many reports and yet it's still not mandatory to stop this from happening."
The Government recently consulted on possible measures it could take to reduce workplace sexual harassment and make it easier for workers to report issues.
Young Women's Trust is calling on the government to:
- put a legal duty on employers to take proactive action to prevent sexual harassment in their workplaces;
- reinstate S 40 of the Equality Act 2010, which made employers liable for harassment of their employees by a third party (such as clients and customers);
- place a legal duty on employers and organisations to protect interns and volunteers from sexual harassment; and
- extend the three-month time limit for employees to bring tribunal cases under the Equality Act to at least six months.
Alongside this, employers should make it easier to report abuse by customers and clients, as well as colleagues, and put in place unbiased reporting processes that do not penalise victims, added Walker.