Under the proposal, 10 single-use plastic products would be banned by 2021 and EU states obliged to recycle 90% of plastic bottles by 2025.
After the vote was carried by 571-53 on Wednesday, the Member of the European Parliament (MEP) who proposed the bill, Frederique Ries, tweeted that it was "a victory for our oceans, for the environment and for future generations."
"We have adopted the most ambitious legislation against single-use plastics," she was quoted as saying in a statement posted on the parliament's website.
"It is essential in order to protect the marine environment and reduce the costs of environmental damage attributed to plastic pollution in Europe, estimated at 22 billion euros ($25bn) by 2030."
The European Commission proposed the ban in May. It will need to be approved by member states after negotiations, which Ries is optimistic will be successful.
"It is up to us now to stay the course in the upcoming negotiations with the Council, due to start as early as November," she said.
China last year banned the imports of 24 varieties of solid waste, including types of plastic and unsorted paper, putting pressure on Europe to deal with its own waste.
The World Economic Forum estimates that there are about 150 million tons of plastic in the world's seas. A study published in Science in 2015 suggested that between five and 13 million tons more are flowing into them every year.
Research shows there will be more plastic than fish by weight in the world's oceans by 2050, which has spurred policy makers, individuals and companies into action.