About a third of all women in the EU have experienced either physical or sexual violence since the age of 15, according to a survey by the European Union Agency for Fundamental Rights.
That corresponds to 62 million women, the survey says.
It is said to be the biggest survey conducted on the subject, and is based on interviews with 42,000 women.
The report calls on EU countries to treat domestic violence as a public, not a private issue.
It says laws and policies relating to sexual harassment should be reviewed.
The survey asked women about their experiences of physical, sexual and psychological violence, at home and in the workplace, as well as stalking, sexual harassment and violence in childhood.
It found that "one in 10 women has experienced some form of sexual violence since the age of 15, and one in 20 has been raped".
The survey noted that 22% had suffered from physical or sexual violence by a partner, but that 67% did not report the most serious incidents of domestic violence to the police.
It said there was a link between heavy alcohol use and domestic violence.
About 18% of women said they had been the victims of stalking since the age of 15, and 55% said they had been sexually harassed, often in the workplace, the survey found.
It noted that young women as a group "are particularly vulnerable to victimisation".
The countries where women reported the highest number of incidences of physical and sexual violence were
- Denmark (52%), Finland (47%) and Sweden (46%), states that are often commended for gender equality.
- The UK and France reported the 5th highest number with 44%
- The lowest incidences of violence were reported in Poland with 19%.
But the survey noted that the results may reflect the fact that some countries find it less culturally acceptable to talk about the problem than others.
"What emerges is a picture of extensive abuse that affects many women's lives, but is systematically under-reported to the authorities," said Morten Kjaerum, director of the Agency for Fundamental Rights.
He said the survey showed that "violence against women is an extensive human rights abuse in all EU member states".
He urged countries to take action to fight the problem, which he said "impacts on society every day".
The report said that campaigns and responses to the problem should be aimed at men as well as women.
"Men need to be positively engaged in initiatives that confront how some men use violence against women."