We study the general evolution of spherical overdensities for the thawing class of dark energy models. We model dark energy with scalar fields having canonical as well as non-canonical kinetic energy. For the non-canonical case, we consider models where the kinetic energy is of the Born–Infeld form. We study various potentials such as linear, inverse-square, exponential as well as PNGB type. We also consider the case where dark energy is homogeneous as well as the case where it is inhomogeneous and virializes together with matter. Our study shows that models with a linear potential, in particular those with a Born–Infeld type kinetic term, can have a significant deviation from the ΛCDM model in terms of density contrast at the time of virialization. Although our approach is a simplified one to study the non-linear evolution of matter overdensities inside the cluster and is not applicable to the actual physical situation, it gives some interesting insights into the non-linear clustering of matter in the presence of the thawing class of dark energy models.