Observations of strong internal waves (IWs) off the Amazon Shelf by the Surface Water and Ocean Topography (SWOT) mission are analyzed. Distinct IWs signatures with wavelengths ranging from 3 to 50 km in coincident sea surface height anomalies (SSHA) and near-nadir normalized radar cross section (NRCS) are clearly identified. Using a three-layer approximation to describe the upper ocean stratification, SWOT SSHAs are converted to IW-induced thermocline displacements, reaching up to 80 m amplitude. This confirms SWOT’s unique ability to quantitatively inform about the state of the ocean interior, the energy and depth distribution of IWs. Moreover, joint SWOT measurements of SSHAs and NRCS further provide new means to precisely study the mechanisms leading to identify IWs from radar intensity measurements. SWOT data can indeed be analyzed in terms of a modulation transfer function (MTF), relating the SWOT NRCS contrasts to divergence of IW surface currents derived from SWOT SSHA measurements. Thanks to these new observations, SWOT-based MTF estimates are derived to quantify relationships between the NRCS contrasts, the amplitude and wavenumber of IWs, and the local wind conditions. In particular, it is shown that the maximum SWOT NRCS contrasts occur when IWs propagate in the wind direction, corresponding to resonant conditions between short wind waves and internal waves.