The amount of genetic variation discovered and characterized in human populations is huge, and is growing rapidly with the widespread availability of modern sequencing technologies. Such a great deal of variation data, that accounts for human diversity, leads to various challenging computational tasks, including variant calling and genotyping of newly sequenced individuals. The standard pipelines for addressing these problems include read mapping, which is a computationally expensive procedure. A few mapping-free tools were proposed in recent years to speed up the genotyping process. While such tools have highly efficient run-times, they focus on isolated, bi-allelic SNPs, providing limited support for multi-allelic SNPs, indels, and genomic regions with high variant density.To address these issues, we introduce MALVA, a fast and lightweight mapping-free method to genotype an individual directly from a sample of reads. MALVA is the first mapping-free tool that is able to genotype multi-allelic SNPs and indels, even in high density genomic regions, and to effectively handle a huge number of variants such as those provided by the 1000 Genome Project. An experimental evaluation on whole-genome data shows that MALVA requires one order of magnitude less time to genotype a donor than alignment-based pipelines, providing similar accuracy. Remarkably, on indels, MALVA provides even better results than the most widely adopted variant discovery tools.