Protected agriculture boosts the production of vegetables, berries and fruits, and it plays a pivotal role in guaranteeing food security globally in the face of climate change. Remote sensing is proven to be useful for identifying the presence of (low-tech) plastic greenhouses and plastic mulches. However, the classification accuracy notoriously decreases in the presence of small-scale farming, heterogeneous land cover and unaccounted seasonal management of protected agriculture. Here, we present the random forest-based pixel-level Open field and Protected Agriculture land cover Classifier (OPAC) developed using Sentinel-2 L2A data. OPAC is trained using tiles from Switzerland over 2 years and the Almeria region in Spain over 1 acquisition day. OPAC classifies eight land covers typical of open field and protected agriculture (plastic mulches, low-tech greenhouses and for the first time high-tech greenhouses). Finally, we assess (1) how the land covers in OPAC are labelled in the Sentinel-2 Scene Classification Layer (SCL) and (2) the correspondence between pixels classified as protected agriculture by OPAC and by the best performing Advanced Plastic Greenhouse Index (APGI). To reduce anthropogenic land covers, we constrain the classification task to agricultural areas retrieved from cadastral data or the Corine Land Cover map. The 5-fold cross-validation reveals an overall accuracy of 92% but other classification scores are moderate when keeping the separation among the three classes of protected agriculture. However, all scores substantially improve upon grouping the three classes into one (with an Intersection Over Union of 0.58 as an average among the scores of the three classes and of 0.98 for one single class). Given the recently acknowledged importance of Sentinel-2 Band 1 (central wavelength of 443 nm), the classification accuracy of OPAC for the Swiss small-scale farming is mostly limited by the band's reduced spatial accuracy (60 m). A careful visual assessment indicates that OPAC achieves satisfactory generalization capabilities also in North European (the Netherlands) and four Mediterranean areas (Spain, Italy, Crete and Turkey) without the need of adding location and temporal specific information. There is good agreement among natural land covers classified by OPAC and the SCL. However, the SCL does not have a class for protected agriculture, the latter being often classified as clouds. APGI achieved similar to lower classification accuracies than OPAC. Importantly, the APGI classification task depends on a user-defined space- and time-specific threshold, whereas OPAC does not. Therefore, OPAC paves the way for rapid mapping of protected agriculture at continental scale.