The estimation of sinkhole-induced ground displacement is an important issue for monitoring soil structures. Distributed optical fiber sensors (DOFSs) composed of an interrogator based on scattering effects in an optical fiber cable sensing element can be used to assess ground displacement. These sensors provide longitudinal strain measurements of the soil structure. This paper proposes a methodology that enables the estimation of displacement fields in the soil structure when a sinkhole appears. It also exposes an experiment that was carried out to create an artificial sinkhole instrumented by optical fiber sensors. This is the first time that those sensors are used to provide submillimeter vertical displacements. The first step of the methodology is to model the ground displacement under 2-D conditions. The longitudinal strain measured by a DOFS can thus be linked to the displacement of the structure. This model is described by the following parameters: 1) the spatial extent of the displacement signature; 2) a coefficient that depends on the interface between the optical fiber cable and the soil; 3) the depth of the sinkhole; and 4) the maximal vertical displacement. The second step consists of the estimation of each parameter independently. The spatial extension is given by fitting the measured strain signature with the empirical model. The depth of the sinkhole can be determined by the measurement of the spatial extension of the ground-displacement profile at several observation depths in the structure. Finally, the vertical maximal displacement is furnished with high precision.