River systems connect the terrestrial biosphere, the atmosphere and the ocean in the global carbon cycle. A recent estimate suggests that up to 3 petagrams of carbon per year could be emitted as carbon dioxide (CO₂) from global inland waters, offsetting the carbon uptake by terrestrial ecosystems. It is generally assumed that inland waters emit carbon that has been previously fixed upstream by land plant photosynthesis, then transferred to soils, and subsequently transported downstream in run-off. But at the scale of entire drainage basins, the lateral carbon fluxes carried by small rivers upstream do not account for all of the CO₂ emitted from inundated areas downstream. Three-quarters of the world's flooded land consists of temporary wetlands, but the contribution of these productive ecosystems to the inland water carbon budget has been largely overlooked. Here we show that wetlands pump large amounts of atmospheric CO₂ into river waters in the floodplains of the central Amazon. Flooded forests and floating vegetation export large amounts of carbon to river waters and the dissolved CO₂ can be transported dozens to hundreds of kilometres downstream before being emitted. We estimate that Amazonian wetlands export half of their gross primary production to river waters as dissolved CO₂ and organic carbon, compared with only a few per cent of gross primary production exported in upland (not flooded) ecosystems. Moreover, we suggest that wetland carbon export is potentially large enough to account for at least the 0.21 petagrams of carbon emitted per year as CO₂ from the central Amazon River and its floodplains. Global carbon budgets should explicitly address temporary or vegetated flooded areas, because these ecosystems combine high aerial primary production with large, fast carbon export, potentially supporting a substantial fraction of CO₂ evasion from inland waters.