Non-invasive prenatal testing (NIPT) is a recent and rapidly evolving method for detecting genetic lesions, such as aneuploidies, of a fetus. However, there is a need for faster and cheaper laboratory and analysis methods to make NIPT more widely accessible. We have developed a novel software package for detection of fetal aneuploidies from next-generation low-coverage whole genome sequencing data. Our tool - NIPTmer - is based on counting pre-defined per-chromosome sets of unique k-mers from raw sequencing data, and applying linear regression model on the counts. Additionally, the filtering process used for k-mer list creation allows one to take into account the genetic variance in a specific sample, thus reducing the source of uncertainty. The processing time of one sample is less than 10 CPU-minutes on a high-end workstation. NIPTmer was validated on a cohort of 583 NIPT samples and it correctly predicted 37 non-mosaic fetal aneuploidies. NIPTmer has the potential to reduce significantly the time and complexity of NIPT post-sequencing analysis compared to mapping-based methods. For non-commercial users the software package is freely available at http://bioinfo.ut.ee/NIPTMer/ .