Closure and seal inspection is one of the key steps in quality control of pizza packages. This is generally carried out by human operators that are not able to inspect all the packages due to cadence restrictions. To overcome this limitation, a computer vision system that automatically performs 100% inline seal and closure inspection is proposed. In this paper, after evaluating pizza package features, the manual quality control procedure, and the packaging machines of a real industrial scenario, a detailed description of hardware and software components of the proposed system as well as the main design decisions are presented. Focusing on the hardware, line-scan technology and hyperspectral imaging has been considered to ensure that all relevant information can be acquired independently of the pizza brand, topping, and film features. Focusing on the software, this applies a three-phases strategy that, first, applies a set of basic rejection controls; second, identifies the sealing region; and third, prepares the data for prediction through the classification of the pizzas using a deep learning network. This network is one of the software key elements and has been selected after comparing the commercial off-the-shelf (pretrained-dl-classifier-resnet50 from MVTec Halcon) and the custom-developed (ResNet18) architectures designed to automate the accept/reject classification of pizza packages. To train the networks, a classification of pizza package defects, focusing on sealing and closure, and an image-based method able to automatically detect them have been proposed. The system has been tested in laboratory and in real industrial conditions comparing it with the manual scenario and considering three pizza brands with two toppings per brand. From the evaluation, it has been seen that ResNet18 achieves the best results with mean, maximum, and minimum precision values of 99.87%, 99.95%, and 99.74%, respectively. Moreover, our system achieves twice the throughput rate with respect to the manual scenario, with the guarantee that all pizzas are evaluated, which is not possible in the manual scenario due to operator fatigue. The proposed solution can be easily adapted to similar contexts, even considering packages with other shapes.