The k-Nearest Neighbor classifier is one of the most well known methods in data mining because of its effectiveness and simplicity. Due to its way of working, the application of this classifier may be restricted to problems with a certain number of examples, especially, when the runtime matters. However, the classification of large amounts of data is becoming a necessary task in a great number of real-world applications. This topic is known as big data classification, in which standard data mining techniques normally fail to tackle such volume of data. In this contribution we propose a MapReduce-based approach for k-Nearest neighbor classification. This model allows us to simultaneously classify large amounts of unseen cases (test examples) against a big (training) dataset. To do so, the map phase will determine the k-nearest neighbors in different splits of the data. Afterwards, the reduce stage will compute the definitive neighbors from the list obtained in the map phase. The designed model allows the k-Nearest neighbor classifier to scale to datasets of arbitrary size, just by simply adding more computing nodes if necessary. Moreover, this parallel implementation provides the exact classification rate as the original k-NN model. The conducted experiments, using a dataset with up to 1 million instances, show the promising scalability capabilities of the proposed approach.