Passive seismic interferometry has become very popular in recent years in exploration geophysics. However, it has not been widely applied in marine exploration. The purpose of this study is to investigate the internal structure of a quasi-amagmatic portion of the Southwest Indian Ridge by interferometry and to examine the performance and reliability of interferometry in marine explorations. To reach this goal, continuous vertical component recordings from 43 ocean bottom seismometers were analyzed. The recorded signals from 200 station pairs were cross-correlated in the frequency domain. The Bessel function method was applied to extract phase–velocity dispersion curves from the zero crossings of the cross-correlations. An average of all the dispersion curves was estimated in a period band 1–10 s and inverted through a conditional neighborhood algorithm which led to the final 1D S-wave velocity model of the crust and upper mantle. The obtained S-wave velocity model is in good agreement with previous geological and geophysical studies in the region and also in similar areas. We find an average crustal thickness of 7 km with a shallow layer of low shear velocities and high Vp/Vs ratio. We infer that the uppermost 2 km are highly porous and may be strongly serpentinized.