Fruit packaging is a time-consuming task due to its low automation level. The gentle handling required by some kinds of fruits and their natural variations complicates the implementation of automated quality controls and tray positioning for final packaging. In this article, we propose a method for the automatic localization and pose estimation of apples captured by a Red-Green-Blue (RGB) camera using convolutional neural networks. Our pose estimation algorithm uses a cascaded structure composed of two independent convolutional neural networks: one for the localization of apples within the images and a second for the estimation of the three-dimensional rotation of the localized and cropped image area containing an apple. We used a single shot multi-box detector to find the bounding boxes of the apples in the images. Lie algebra is used for the regression of the rotation, which represents an innovation in this kind of application. We compare the performances of four different network architectures and show that this kind of representation is more suitable than using state-of-the-art quaternions. By using this method, we achieved a promising accuracy for the rotation regression of 98.36%, considering an error range lower than 15 degrees, forming a base for the automation of fruit packing systems.