The multifractal analysis has allowed to quantify the genetic variability and non-linear stability along the human genome sequence. It has some implications in explaining several genetic diseases given by some chromosome abnormalities, among other genetic particularities. The multifractal analysis of a genome is carried out by dividing the complete DNA sequence in smaller fragments and calculating the generalized dimension spectrum of each fragment using the chaos game representation and the box-counting method. This is a time consuming process because it involves the processing of large data sets using floating-point representation. In order to reduce the computation time, we designed an application-specific processor, here called multifractal processor, which is based on our proposed hardware-oriented algorithm for calculating efficiently the generalized dimension spectrum of DNA sequences. The multifractal processor was implemented on a low-cost SoC-FPGA and was verified by processing a complete human genome. The execution time and numeric results of the Multifractal processor were compared with the results obtained from the software implementation executed in a 20-core workstation, achieving a speed up of 2.6x and an average error of 0.0003 percent.