Internet memes have emerged as an increasingly popular means of communication on the Web. Although typically intended to elicit humour, they have been increasingly used to spread hatred, trolling, and cyberbullying, as well as to target specific individuals, communities, or society on political, socio-cultural, and psychological grounds. While previous work has focused on detecting harmful, hateful, and offensive memes, identifying whom they attack remains a challenging and underexplored area. Here we aim to bridge this gap. In particular, we create a dataset where we annotate each meme with its victim(s) such as the name of the targeted person(s), organization(s), and community(ies). We then propose DISARM (Detecting vIctimS targeted by hARmful Memes), a framework that uses named entity recognition and person identification to detect all entities a meme is referring to, and then, incorporates a novel contextualized multimodal deep neural network to classify whether the meme intends to harm these entities. We perform several systematic experiments on three test setups, corresponding to entities that are (a) all seen while training, (b) not seen as a harmful target on training, and (c) not seen at all on training. The evaluation results show that DISARM significantly outperforms ten unimodal and multimodal systems. Finally, we show that DISARM is interpretable and comparatively more generalizable and that it can reduce the relative error rate for harmful target identification by up to 9 points absolute over several strong multimodal rivals.