One of the key challenges in the battle against the Coronavirus (COVID-19) pandemic is to detect and quantify the severity of the disease in a timely manner. Computed tomographies (CT) of the lungs are effective for assessing the state of the infection. Unfortunately, labeling CT scans can take a lot of time and effort, with up to 150 minutes per scan. We address this challenge introducing a scalable, fast, and accurate active learning system that accelerates the labeling of CT scan images. Conventionally, active learning methods require the labelers to annotate whole images with full supervision, but that can lead to wasted efforts as many of the annotations could be redundant. Thus, our system presents the annotator with unlabeled regions that promise high information content and low annotation cost. Further, the system allows annotators to label regions using point-level supervision, which is much cheaper to acquire than per-pixel annotations. Our experiments on open-source COVID-19 datasets show that using an entropy-based method to rank unlabeled regions yields to significantly better results than random labeling of these regions. Also, we show that labeling small regions of images is more efficient than labeling whole images. Finally, we show that with only 7% of the labeling effort required to label the whole training set gives us around 90% of the performance obtained by training the model on the fully annotated training set. Code is available at: url{https://github.com/IssamLaradji/covid19_active_learning}.