In this paper, we deal with offensive and abusive language detection on Bambara language, which is an under-resourced language mainly spoken in Mali and some other African countries. As a first work on this language, we aim to release OBAM v1.0 corpus compiling 4k of texts that are labeled as normal, offensive and abusive. In addition, we have carried out a set of experiments with different configurations using various machine learning and deep learning classifiers. In overall, the classifiers produced acceptable results (0.80 and 0.73 of F-score in two-category and three-category classification, respectively), but they could be improved by expanding the corpus and proposing new features.