Taxonomic classification, i.e., the identification and assignment to groups of biological organisms with the same origin and characteristics, is a common task in genetics. Nowadays, taxonomic classification is mainly based on genome similarity search to large genome databases. In this process, the classification quality depends heavily on the database since representative relatives have to be known already. Many genomic sequences cannot be classified at all or only with a high misclassification rate. Here we present BERTax, a program that uses a deep neural network to precisely classify the superkingdom, phylum, and genus of DNA sequences taxonomically without the need for a known representative relative from a database. For this, BERTax uses the natural language processing model BERT trained to represent DNA. We show BERTax to be at least on par with the state-of-the-art approaches when taxonomically similar species are part of the training data. In case of an entirely novel organism, however, BERTax clearly outperforms any existing approach. Finally, we show that BERTax can also be combined with database approaches to further increase the prediction quality. Since BERTax is not based on homologous entries in databases, it allows precise taxonomic classification of a broader range of genomic sequences. This leads to a higher number of correctly classified sequences and thus increases the overall information gain.