Public health research frequently requires the integration of information from different data sources. However, errors in the records and the high computational costs involved make linking large administrative databases using record linkage (RL) methodologies a major challenge. We present Tucuxi-BLAST, a versatile tool for probabilistic RL that utilizes a DNA-encoded approach to encrypt, analyze and link massive administrative databases. Tucuxi-BLAST encodes the identification records into DNA. BLASTn algorithm is then used to align the sequences between databases. We tested and benchmarked on a simulated database containing records for 300 million individuals and also on four large administrative databases containing real data on Brazilian patients. Our method was able to overcome misspellings and typographical errors in administrative databases. In processing the RL of the largest simulated dataset (200k records), the state-of-the-art method took 5 days and 7 h to perform the RL, while Tucuxi-BLAST only took 23 h. When compared with five existing RL tools applied to a gold-standard dataset from real health-related databases, Tucuxi-BLAST had the highest accuracy and speed. By repurposing genomic tools, Tucuxi-BLAST can improve data-driven medical research and provide a fast and accurate way to link individual information across several administrative databases.