Malaria is a life-threatening mosquito-borne disease of global importance, and it is most prevalent in the low-income countries of the developing world. The diagnosis of malaria infection is conventionally performed by laboratorians through visual examination of blood smear images under a microscope. However, the results of such diagnostic testing depend on the laboratory technicians' experience with staining and image interpretation, which can be severely lacking in low-resource settings. Convolutional neural networks (CNNs) have great potential for automated malaria diagnosis from images without the need of human expert interaction. However, studies have shown that current CNNs are not robust to adversarial noises which are small input perturbations that cause CNNs to incorrectly classify medical images. In this study, we developed a CNN for malaria parasite identification and evaluated it on a dataset of 27,558 cell images through patient-level cross validation. To improve robustness against adversarial noises for this application, the structure of the CNN was specially designed to limit the receptive field of the output, and adversarial training was applied with gradually increasing level of noises. Compared to three baseline networks (ResNet-18, MobileNet, and MnasNet) and two variants of the CNN, our custom-designed CNN achieved a substantially lower computation cost and better adversarial robustness against PGD-generated adversarial noises on the malaria image dataset. Our study holds the promise of developing a robust and affordable solution for automated diagnosis of malarial infection.