Measurements of water levels in the main channels of rivers, upland tributaries and floodplain lakes are necessary for understanding flooding hazards, methane production, sediment transport and nutrient exchange. But most remote river basins have only a few gauging stations and these tend to be restricted to large river channels. Although radar remote sensing techniques using interferometric phase measurements have the potential to greatly improve spatial sampling, the phase is temporally incoherent over open water and has therefore not been used to determine water levels. Here we use interferometric synthetic aperture radar (SAR) data, acquired over the central Amazon by the Space Shuttle imaging radar mission, to measure subtle water level changes in an area of flooded vegetation on the Amazon flood plain. The technique makes use of the fact that flooded forests and floodplain lakes with emergent shrubs permit radar double-bounce returns from water and vegetation surfaces, thus allowing coherence to be maintained. Our interferometric phase observations show decreases in water levels of 7-11 cm per day for tributaries and lakes within approximately 20 km of a main channel and 2-5 cm per day at distances of approximately 80 km. Proximal floodplain observations are in close agreement with main-channel gauge records, indicating a rapid response of the flood plain to decreases in river stage. With additional data from future satellite missions, the technique described here should provide direct observations important for understanding flood dynamics and hydrologic exchange between rivers and flood plains.