The study – released ahead of the 75th anniversary of Kristallnacht, which saw Nazi thugs smash up Jewish businesses and synagogues – found that 66% of European Jews considered anti-Semitism "a fairly big or very big" problem in their country.
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A total of 76% said it had worsened in the past five years, with abuse especially prevalent on the Internet, where social media and file-sharing websites allowed anti-Semitism to travel around even faster than before.
"I feel that since going on Facebook, I have experienced more anti-Semitic comments in a few years than I ever have done throughout my whole life," one British respondent was quoted as saying. "This is very dispiriting."
FRA's report was based on an online survey in eight EU countries – Belgium, Britain, France, Germany, Hungary, Italy, Latvia and Sweden – which are home to 90% of the bloc's Jewish population.
Of these, France, Belgium and Hungary reported the highest rates of anti-Semitism in the media and political life, as well vandalism and open hostility in the street.
Hungary, especially, has come under fire in the past year over repeated anti-Semitic incidents, which critics say Prime Minister Viktor Orban has done little to fight.
"Anti-Semitism is a disturbing example of how prejudice can persist through the centuries, and it has no place in our society today," FRA director Morten Kjaerum said in the report.
"It is particularly distressing to see that the Internet, which should be a tool for communication and dialogue, is being used as an instrument of anti-Semitic harassment," he added.
About quarter of Jews afraid to express Jewishness
According to FRA's study, 21% of people said they had experienced verbal or physical abuse in the last year for being Jewish.
Close to half meanwhile feared public insults or harassment in the next 12 months, with as many as 23% saying they purposely avoided Jewish sites or celebrations as they might not be safe there.
"We are asked to disperse quickly at the exit of the synagogues, community centers... a special security service is required, which is, to my knowledge, not necessary at the exit of the churches or chaplaincies... nor for temples and mosques," one French woman was quoted in the survey.
Such constraints on day-to-day living and a feeling of insecurity had pushed almost a third of respondents to consider emigrating, FRA found.
The European Jewish Congress quickly welcomed the report.
"However the fact that a quarter of Jews are not able to express their Jewishness because of fear should be a watershed moment for the continent of Europe and the European Union," said its president Moshe Kantor.
The fact that 82% of people did not report abuse or discrimination they had experienced to the authorities was "the most damning indictment of the report," he added.
"European Jewry simply has little faith or trust in the process of law enforcement, legislative or judicial processes on large parts of the continent," he said, calling for improved legislation and other steps to promote tolerance.
Even today, only 13 of the 28 EU states gather data on anti-Semitic incidents, FRA said.
In total, some 5,850 people who identified themselves as Jewish responded to the survey between September and October 2012.