Cloud detection in high-resolution satellite images is a critical step for many remote sensing applications, but also a challenge, as such images have limited spectral bands. The contribution of this paper is twofold: We present a dataset called CloudPeru as well as a methodology for cloud detection in multispectral satellite images (approximately 2.8 meters per pixel) using deep learning. We prove that an agile Convolutional Neural Network (CNN) is able to distinguish between non-clouds and different types of clouds, including thin and very small ones, and achieve a classification accuracy of 99.94%. Each image is subdivided into superpixels by the SLICO algorithm, which are then processed by the trained CNN. Finally, we obtain the cloud mask by applying a threshold of 0.5 on the probability map. The results are compared with manually annotated images, showing a Kappa coefficient of 0.944, which is higher than that of compared methods.