Cyberattacks in the Internet of Things (IoT) are growing exponentially, especially zero-day attacks mostly driven by security weaknesses on IoT networks. Traditional intrusion detection systems (IDSs) adopted machine learning (ML), especially deep Learning (DL), to improve the detection of cyberattacks. DL-based IDSs require balanced datasets with large amounts of labeled data; however, there is a lack of such large collections in IoT networks. This paper proposes an efficient intrusion detection framework based on transfer learning (TL), knowledge transfer, and model refinement, for the effective detection of zero-day attacks. The framework is tailored to 5G IoT scenarios with unbalanced and scarce labeled datasets. The TL model is based on convolutional neural networks (CNNs). The framework was evaluated to detect a wide range of zero-day attacks. To this end, three specialized datasets were created. Experimental results show that the proposed TL-based framework achieves high accuracy and low false prediction rate (FPR). The proposed solution has better detection rates for the different families of known and zero-day attacks than any previous DL-based IDS. These results demonstrate that TL is effective in the detection of cyberattacks in IoT environments.