The long-read sequencing platform MinION, developed by Oxford Nanopore Technologies, enables the sequencing of bacterial genomes in resource-limited settings, such as field conditions or low- and middle-income countries. For this purpose, protocols for extracting high-molecular-weight DNA using nonhazardous, inexpensive reagents and equipment are needed, and some methods have been developed for gram-negative bacteria. However, we found that without modification, these protocols are unsuitable for gram-positive Streptococcus spp., a major threat to fish farming and food security in low- and middle-income countries. Multiple approaches were evaluated, and the most effective was an extraction method using lysozyme, sodium dodecyl sulfate, and proteinase K for lysis of bacterial cells and magnetic beads for DNA recovery. We optimized the method to consistently achieve sufficient yields of pure high-molecular-weight DNA with minimal reagents and time and developed a version of the protocol which can be performed without a centrifuge or electrical power. The suitability of the method was verified by MinION sequencing and assembly of 12 genomes of epidemiologically diverse fish-pathogenic Streptococcus iniae and Streptococcus agalactiae isolates. The combination of effective high-molecular-weight DNA extraction and MinION sequencing enabled the discovery of a naturally occurring 15 kb low-copy number mobilizable plasmid in S. iniae, which we name pSI1. We expect that our resource-limited settings-adapted protocol for high-molecular-weight DNA extraction could be implemented successfully for similarly recalcitrant-to-lysis gram-positive bacteria, and it represents a method of choice for MinION-based disease diagnostics in low- and middle-income countries.