This paper proposes a self-supervised latent space clustering algorithm, called the Deep Latent Space Clustering, for the detection of stealthy false data injection attacks (FDIAs) in smart grids against state estimation algorithms. The stealthy FDI model considered is based on the accurate AC state estimation and is able to bypass conventional bad data detection (BDD) algorithms with ease. The key element of the detection model is a stacked autoencoder network that first undergoes a carefully designed two-step finetuning process, following which a trainable clustering head is stacked on top of the finetuned encoder and the final network is further trained to achieve a clean clustering of the data into benign and compromised samples without labelled supervision. To test the efficacy and scalability of the detection model, it is tested on the standard IEEE 14 bus, 118 bus and 300 bus test systems. The self-supervised clustering model is compared to several supervised, semi-supervised and unsupervised algorithms proposed in the literature for detection of FDI on the aforementioned test cases and has been found to perform at par with the state of the art among them.