"The extent of corruption in Europe is "breathtaking" and it costs the EU economy about 120bn euros (£99bn) annually, the European Commission says.
Writing in Sweden's Goeteborgs-Posten daily, she said corruption was eroding trust in democracy and draining resources from the legal economy.
For the report the Commission studied corruption in all 28 EU member states.
"The extent of the problem in Europe is breathtaking, although Sweden is among the countries with the least problems," Ms Malmstroem wrote.
The Commission says it is the first time it has produced such a report. It also makes recommendations on how to tackle corruption.
Ms Malmstroem said that in some countries public procurement procedures were vulnerable to fraud, while in others party financing was the main problem, or municipal bodies were badly affected. And in some countries patients have to pay bribes in order to get adequate medical care, she wrote.
The study includes two major opinion polls, which indicated that three-quarters of EU citizens consider corruption to be widespread in their country.
Four out of 10 of the businesses surveyed described corruption as an obstacle to doing business in Europe.
In Sweden, 18% of people surveyed said they knew someone who had received a bribe, compared with a European average of 12%, Ms Malmstroem said.
Despite that finding, she said Sweden "is undoubtedly one of the countries with the least problems with corruption, and other EU countries should learn from Sweden's solutions for dealing with the problem", pointing to the role of laws on transparency and openness."