The recently introduced Oxford Nanopore MinION platform generates DNA sequence data in real-time. This opens immense potential to shorten the sample-to-results time and is likely to lead to enormous benefits in rapid diagnosis of bacterial infection and identification of drug resistance. However, there are very few tools available for streaming analysis of real-time sequencing data. Here, we present a framework for streaming analysis of MinION real-time sequence data, together with probabilistic streaming algorithms for species typing, multi-locus strain typing, gene presence strain-typing and antibiotic resistance profile identification. Using three culture isolate samples as well as a mixed-species sample, we demonstrate that bacterial species and strain information can be obtained within 30 minutes of sequencing and using about 500 reads, initial drug-resistance profiles within two hours, and complete resistance profiles within 10 hours. Multi-locus strain typing required more than 15x coverage to generate confident assignments, whereas gene-presence typing could detect the presence of a known strain with 0.5x coverage. We also show that our pipeline can process over 100 times more data than the current throughput of the MinION on a desktop computer.