Owing the epidemic of the novel coronavirus disease 2019 (COVID-19), chest X-ray computed tomography imaging is being used for effectively screening COVID-19 patients. The development of computer-aided systems based on deep neural networks (DNNs) has become an advanced open source to rapidly and accurately detect COVID-19 cases because the need for expert radiologists, who are limited in number, forms a bottleneck for screening. However, thus far, the vulnerability of DNN-based systems has been poorly evaluated, although realistic and high-risk attacks using universal adversarial perturbation (UAP), a single (input image agnostic) perturbation that can induce DNN failure in most classification tasks, are available. Thus, we focus on representative DNN models for detecting COVID-19 cases from chest X-ray images and evaluate their vulnerability to UAPs. We consider non-targeted UAPs, which cause a task failure, resulting in an input being assigned an incorrect label, and targeted UAPs, which cause the DNN to classify an input into a specific class. The results demonstrate that the models are vulnerable to non-targeted and targeted UAPs, even in the case of small UAPs. In particular, the 2% norm of the UAPs to the average norm of an image in the image dataset achieves >85% and >90% success rates for the non-targeted and targeted attacks, respectively. Owing to the non-targeted UAPs, the DNN models judge most chest X-ray images as COVID-19 cases. The targeted UAPs allow the DNN models to classify most chest X-ray images into a specified target class. The results indicate that careful consideration is required in practical applications of DNNs to COVID-19 diagnosis; in particular, they emphasize the need for strategies to address security concerns. As an example, we show that iterative fine-tuning of DNN models using UAPs improves the robustness of DNN models against UAPs.