MOTIVATION: Gapped k-mer kernels with support vector machines (gkm-SVMs) have achieved strong predictive performance on regulatory DNA sequences on modestly sized training sets. However, existing gkm-SVM algorithms suffer from slow kernel computation time, as they depend exponentially on the sub-sequence feature length, number of mismatch positions, and the task's alphabet size. RESULTS: In this work, we introduce a fast and scalable algorithm for calculating gapped k-mer string kernels. Our method, named FastSK, uses a simplified kernel formulation that decomposes the kernel calculation into a set of independent counting operations over the possible mismatch positions. This simplified decomposition allows us to devise a fast Monte Carlo approximation that rapidly converges. FastSK can scale to much greater feature lengths, allows us to consider more mismatches, and is performant on a variety of sequence analysis tasks. On multiple DNA transcription factor binding site prediction datasets, FastSK consistently matches or outperforms the state-of-the-art gkmSVM-2.0 algorithms in area under the ROC curve, while achieving average speedups in kernel computation of ∼100× and speedups of ∼800× for large feature lengths. We further show that FastSK outperforms character-level recurrent and convolutional neural networks while achieving low variance. We then extend FastSK to 7 English-language medical named entity recognition datasets and 10 protein remote homology detection datasets. FastSK consistently matches or outperforms these baselines. AVAILABILITY AND IMPLEMENTATION: Our algorithm is available as a Python package and as C++ source code at https://github.com/QData/FastSK. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.