Automated detection and segmentation of pulmonary nodules on lung computed tomography (CT) scans can facilitate early lung cancer diagnosis. Existing supervised approaches for automated nodule segmentation on CT scans require voxel-based annotations for training, which are labor- and time-consuming to obtain. In this work, we propose a weakly-supervised method that generates accurate voxel-level nodule segmentation trained with image-level labels only. By adapting a convolutional neural network (CNN) trained for image classification, our proposed method learns discriminative regions from the activation maps of convolution units at different scales, and identifies the true nodule location with a novel candidate-screening framework. Experimental results on the public LIDC-IDRI dataset demonstrate that, our weakly-supervised nodule segmentation framework achieves competitive performance compared to a fully-supervised CNN-based segmentation method.