DNA sequencing plays an important role in the bioinformatics research community. DNA sequencing is important to all organisms, especially to humans and from multiple perspectives. These include understanding the correlation of specific mutations that plays a significant role in increasing or decreasing the risks of developing a disease or condition, or finding the implications and connections between the genotype and the phenotype. Advancements in the high-throughput sequencing techniques, tools, and equipment, have helped to generate big genomic datasets due to the tremendous decrease in the DNA sequence costs. However, the advancements have posed great challenges to genomic data storage, analysis, and transfer. Accessing, manipulating, and sharing the generated big genomic datasets present major challenges in terms of time and size, as well as privacy. Data size plays an important role in addressing these challenges. Accordingly, data minimization techniques have recently attracted much interest in the bioinformatics research community. Therefore, it is critical to develop new ways to minimize the data size. This paper presents a new real-time data minimization mechanism of big genomic datasets to shorten the transfer time in a more secure manner, despite the potential occurrence of a data breach. Our method involves the application of the random sampling of Fourier transform theory to the real-time generated big genomic datasets of both formats: FASTA and FASTQ and assigns the lowest possible code-word to the most frequent characters of the datasets. Our results indicate that the proposed data minimization algorithm is up to 79% of FASTA datasets' size reduction, with 98-fold faster and more secure than the standard data-encoding method. Also, the results show up to 45% of FASTQ datasets' size reduction with 57-fold faster than the standard data-encoding approach. Based on our results, we conclude that the proposed data minimization algorithm provides the best performance among current data-encoding approaches for big real-time generated genomic datasets.