Today, fake information has become a significant problem, exacerbated by the acceleration of access to information. The spread of fake information has a dangerous impact, especially regarding global health issues, for example COVID-19. People can access various resources to obtain information, including online sites and social media. One of the methods to control the spread of false information is detecting hoaxes. Many methods have been developed to identify hoaxes; most previous studies have focused on developing hoax detection methods using data from a single source in English. The present study is carried out to detect fake news in Indonesian language using multiple data sources, including traditional and social media in the context of COVID-19. The study uses Long Short-Term Memory (LSTM) and the Robustly Optimised Bidirectional Encoder Representations from Transformers Pre-Training Approach (RoBERTa). The LSTM approach is used to develop four different architectures that varied based on: (1) the use of text-only versus the use of both title and text; (2) the number of LSTM and dense layers; and (3) the activation function. The LSTM model with text-only data, a single LSTM layer and two dense layers, outperformed other LSTM architectures, achieving the highest accuracy of 92.17%. The LSTM models require a considerably short training time of 23–27 minutes for 3,847 articles and has a detection time of 3.8–4.1 ms per article. The RoBERTa classifiers outperformed all LSTM models with an accuracy of over 97% and a significantly better training time, with a margin of more than 50% compared to LSTM classifiers, although it had a slightly longer test time. Both LSTM and RoBERTa models outperformed the Naïve Bayes and SVM benchmark methods in terms of accuracy, precision, and recall. Therefore, this study shows that both LSTM and RoBERTa methods are reliable and can be reasonably implemented for real-time fake news detection.