The integration of photovoltaic (PV) panels has allowed power distribution systems (PDSs) to regulate their voltage through the injection/absorption of reactive power. The deployment of information and communication technologies (ICTs), which is required for this scheme, has made the PDS prone to various cyber threats, e.g., false data injection (FDI) attacks. To counter these attacks, this paper proposes a data-driven framework to detect FDI attacks against voltage regulation of PV-integrated PDS. Initially, an attack-free system is modeled along with its voltage regulation scheme, where the grid measurements are sent to a centralized controller and the control signals are transmitted back to PVs to be used by their local controllers. Then, a convolutional neural network (CNN) framework is proposed to detect FDI attacks. To train this framework-which should be able to distinguish between normal grid behaviors and attacks-a complete and realistic dataset is formed to cover all normal conditions and unpredictable changes of a PDS during a year. Since normal variations and fluctuations in power consumption lead to changes in the voltage profile, this dataset is enriched using features such as season, weekdays, weekends, load conditions, and PV generation power. The performance of the trained framework has been compared with other supervised Machine Learning-based and deep-learning techniques for FDI attacks against modified IEEE 33-and 141bus PDSs. Simulation results demonstrate the superior performance of the proposed framework in detecting FDI attacks.