Recent research has shown that the security of power grids can be seriously threatened by botnet-type cyber attacks that target a large number of high-wattage smart electrical appliances owned by end-users. Accurate detection and localization of such attacks is of critical importance in limiting the damage. To this end, the paper proposes a novel technique using capsule networks (CNs) tailored to the power grid security application that uses the frequency and phase angle data monitored by phasor measurement units (PMUs). With the benefit of vector output from capsules and dynamic routing agreements between them, CNs can obtain accurate detection and localization performance. To demonstrate the efficiency of the suggested technique, we compare the developed CN with benchmark data-driven methodologies, including two-dimensional convolutional neural networks (2D-CNN), one-dimensional CNN (1D-CNN), deep multi-layer perceptrons (MLP), and support vector machines (SVM). Simulations are performed on IEEE 14-, 39-, and 57-bus systems, considering various real-world issues such as PMU delays, noisy data, and missing data points. The results show that CNs significantly outperform other techniques, thus making them suitable for the aforementioned cyber security applications.