Plasmodium malaria is a parasitic protozoan that causes malaria in humans. Computer aided detection of Plasmodium is a research area attracting great interest. In this paper, we study the performance of various machine learning and deep learning approaches for the detection of Plasmodium on cell images from digital microscopy. We make use of a publicly available dataset composed of 27,558 cell images with equal instances of parasitized (contains Plasmodium) and uninfected (no Plasmodium) cells. We randomly split the dataset into groups of 80% and 20% for training and testing purposes, respectively. We apply color constancy and spatially resample all images to a particular size depending on the classification architecture implemented. We propose a fast Convolutional Neural Network (CNN) architecture for the classification of cell images. We also study and compare the performance of transfer learning algorithms developed based on well-established network architectures such as AlexNet, ResNet, VGG-16 and DenseNet. In addition, we study the performance of the bag-of-features model with Support Vector Machine for classification. The overall probability of a cell image comprising Plasmodium is determined based on the average of probabilities provided by all the CNN architectures implemented in this paper. Our proposed algorithm provided an overall accuracy of 96.7% on the testing dataset and area under the Receiver Operating Characteristic (ROC) curve value of 0.994 for 2756 parasitized cell images. This type of automated classification of cell images would enhance the workflow of microscopists and provide a valuable second opinion.