Forests from Spain to Sweden are getting older, packed with trees less able to soak up CO2 emissions, which are blamed for rising world temperatures, rising sea levels and increased heatwave and flood risk, experts said.
Trees are being threatened by more fires, storms and insect attacks, said the study published in the journal Nature Climate Change.
Some parts of the continent have also started cutting down some forests, it added.
This means that Europe should no longer assume its forests will be able to continue absorbing carbon emissions from factories, power plants and cars, at the same rate. Forests are currently thought to absorb about 10% of Europe's emissions.
"These regrowing forests have shown to be a persistent carbon sink, projected to continue for decades, however, there are early signs of saturation. Forest policies and management strategies need revision if we want to sustain the sink," the Nature Climate Change report said.
Back-of-the-envelope calculations suggested saturation point could be reached by around 2030 unless governments took action, said Gert-Jan Nabuurs, of Wageningen University and Research in the Netherlands, who led the study with experts in Finland, Switzerland and Italy.
Europe is in its greenest state for centuries, with forests probably covering the largest area since Medieval times - largely thanks to a rush of planting to rebuild the continent after the ravages of World War Two, the report said.
But data since 2005 showed the growth of those forests was now slowing as their trees got older.
Trees absorb carbon from the air into their trunks, roots and branches. As they grow older, this absorption lessens and the stored carbon is released when they die and rot.
Man-made emissions of carbon dioxide, a heat-trapping gas that is released by burning fossil fuels, are very likely to be the main cause of rising temperatures since 1950, a U.N. panel of climate experts says.
Better management could help avert the problem of Europe's aging forests, Nabuurs said. The authors also recommended selective harvesting and more new forests.
Annemarie Bastrup-Birk, a forestry expert who works at the European Environment Agency in Copenhagen who was also an author of that report, said the decline in forest growth was mainly in France and Germany with continued gains elsewhere.
"It's still very regional," she said, warning that the Nature Climate Change study might be premature in raising concerns about a continent-wide problem.
The EU plans to cut its overall greenhouse gas emissions by 20 percent below 1990 levels by 2020 as part of international efforts to slow global warming. Each nation can count the uptake of carbon in forests towards the total.
An international report on the state of Europe's forests in 2011 said the net annual increase in living tree wood in the European Union slowed to 609 million cubic metres in 2010 from 620 million in 2005.