Continual (incremental) learning approaches are designed to address catastrophic forgetting in neural networks by training on batches or streaming data over time. In many real-world scenarios, the environments that generate streaming data are exposed to untrusted sources. These untrusted sources can be exposed to data poisoned by an adversary. The adversaries can manipulate and inject malicious samples into the training data. Thus, the untrusted data sources and malicious samples are meant to expose the vulnerabilities of neural networks that can lead to serious consequences in applications that require reliable performance. However, recent works on continual learning only focused on adversary agnostic scenarios without considering the possibility of data poisoning attacks. Further, recent work has demonstrated there are vulnerabilities of continual learning approaches in the presence of backdoor attacks with a relaxed constraint on manipulating data. In this paper, we focus on a more general and practical poisoning setting that artificially forces catastrophic forgetting by clean-label data poisoning attacks. We proposed a task targeted data poisoning attack that forces the neural network to forget the previous-learned knowledge, while the attack samples remain stealthy. The approach is benchmarked against three state-of-the-art continual learning algorithms on both domain and task incremental learning scenarios. The experiments demonstrate that the accuracy on targeted tasks significantly drops when the poisoned dataset is used in continual task learning.