Predicting how different interventions will causally affect a specific individual is important in a variety of domains such as personalized medicine, public policy, and online marketing. However, most existing causal methods cannot generalize to predicting the effects of previously unseen interventions (e.g., a newly invented drug), because they require data for individuals who received the intervention. Here, we consider zero-shot causal learning: predicting the personalized effects of novel, previously unseen interventions. To tackle this problem, we propose CaML, a causal meta-learning framework which formulates the personalized prediction of each intervention's effect as a task. Rather than training a separate model for each intervention, CaML trains as a single meta-model across thousands of tasks, each constructed by sampling an intervention and individuals who either did or did not receive it. By leveraging both intervention information (e.g., a drug's attributes) and individual features (e.g., a patient's history), CaML is able to predict the personalized effects of unseen interventions. Experimental results on real world datasets in large-scale medical claims and cell-line perturbations demonstrate the effectiveness of our approach. Most strikingly, CaML zero-shot predictions outperform even strong baselines which have direct access to data of considered target interventions.