In this paper, we address the change-point estimation issue in multivariate observations which consist in functions having piecewise constant first derivatives corrupted by some additional noise. We propose to solve this problem by rewriting it as a variable selection issue in a sparse multivariate linear model. Moreover, the methodology that we propose takes into account the dependence that may exist within the multivariate observations. Then, the performance of our approach is assessed through some numerical experiments and compared to other alternative and classical methods. Finally, we apply our methodology to experimental data in order to study the vegetative development of oilseed rape. The evolution of the number of leaves of oilseed rape can be modeled as a function having piecewise constant first derivatives corrupted by some additional noise where the change-points correspond to key times in the plant phenology. Our novel estimation method increases the accuracy of the change-point estimation in comparison with classical approaches. Moreover, we show that the parameters of the covariance matrix depend on the level of competition between plants.