An internal briefing document seen by the BBC says the effects of globalisation on advanced economies is "often uneven" and "may have led to rising wage inequality".
The bank, which provides loans to developing countries, also says that "adjustment costs", such as helping people who have lost their jobs, have been higher than expected.
Dr Jim Kim, the head of the World Bank, told the BBC that he understood why people were angry in advanced economies despite the fact that free trade was one of the "most powerful" drivers of growth and prosperity.
"I hear them and they are saying that my life is not better than my parents and my children's life does not look like it's going to be better than mine," he told me.
"So there is a real concern but the answer is to have more robust social security programmes, so you have a safety net. And then you need to get serious about getting the skills you need for the jobs of the future."
Dr Kim said that 20% of jobs lost in advanced economies could be linked to trade, with the rest down to automation and the need for new skills.
He said governments needed to do more to support those who had lost their jobs.
The document, written by World Bank economists, does say that "trade has played a powerful role in creating jobs and contributing to rising incomes in advanced economies", as well as in emerging economies.
But it highlights problems that have been created.
"Recent evidence for the US suggests that adjustment costs for those employed in sectors exposed to import competition from China are much higher than previously thought," the document says.
"While trade may have contributed to rising inequality in high income economies, so has technological change and the weakening of institutions that used to represent the interests of labour.
"Given overall efficiency gains, the dislocation effects of trade in advanced economies must be addressed through stronger safety nets and enhanced skills and flexible labour markets."
Dr Kim said that if developed countries start throwing up trade barriers, ambitious targets to eradicate poverty by 2030 could be missed because global economic growth would be slower.
"It will be much, much harder to achieve [the poverty targets], there's no question," Dr Kim told me.
"We can build all the infrastructure we want and we can increase trade among the emerging market countries, [but] at the end of the day if global trade does not grow at a more robust rate it is going to be very hard to make those targets.
"If all the developed countries close their borders, it's going to be very difficult and it's going to be very difficult for those countries as well."
I asked him directly if the target could be missed.
"We very well could, absolutely, it's possible," he said.
Proposals to end extreme poverty - defined as anyone living on less than $1.25 a day - were put together by a United Nations committee chaired by David Cameron in 2013.
Dr Kim said that action by organisations like the World Bank, which provides loans to developing countries, as well as the growth of free trade had lifted millions of people out of poverty.
He said that international organisations had to do more to explain the advantages of global trade for advanced as well as emerging economies.
Source: BBC Business News