To aid humans in everyday tasks, robots need to know which objects exist in the scene, where they are, and how to grasp and manipulate them in different situations. Therefore, object recognition and grasping are two key functionalities for autonomous robots. Most state-of-the-art approaches treat object recognition and grasping as two separate problems, even though both use visual input. Furthermore, the knowledge of the robot is fixed after the training phase. In such cases, if the robot encounters new object categories, it must be retrained to incorporate new information without catastrophic forgetting. In order to resolve this problem, we propose a deep learning architecture with an augmented memory capacity to handle open-ended object recognition and grasping simultaneously. In particular, our approach takes multi-views of an object as input and jointly estimates pixel-wise grasp configuration as well as a deep scale- and rotation-invariant representation as output. The obtained representation is then used for open-ended object recognition through a meta-active learning technique. We demonstrate the ability of our approach to grasp never-seen-before objects and to rapidly learn new object categories using very few examples on-site in both simulation and real-world settings. A video of these experiments is available online at: https://youtu.be/n9SMpuEkOgk