Meta-learning is a promising strategy for learning to efficiently learn using data gathered from a distribution of tasks. However, the meta-learning literature thus far has focused on the task segmented setting, where at train-time, offline data is assumed to be split according to the underlying task, and at test-time, the algorithms are optimized to learn in a single task. In this work, we enable the application of generic meta-learning algorithms to settings where this task segmentation is unavailable, such as continual online learning with unsegmented time series data. We present meta-learning via online changepoint analysis (MOCA), an approach which augments a meta-learning algorithm with a differentiable Bayesian changepoint detection scheme. The framework allows both training and testing directly on time series data without segmenting it into discrete tasks. We demonstrate the utility of this approach on three nonlinear meta-regression benchmarks as well as two meta-image-classification benchmarks.