Structural variants (SVs) can promote speciation by directly causing reproductive isolation or by suppressing recombination across large genomic regions. Whereas examples of each mechanism have been documented, systematic tests of the role of SVs in speciation are lacking. Here, we take advantage of long-read (Oxford nanopore) whole-genome sequencing and a hybrid zone between two Lycaeides butterfly taxa (L. melissa and Jackson Hole Lycaeides) to comprehensively evaluate genome-wide patterns of introgression for SVs and relate these patterns to hypotheses about speciation. We found >100,000 SVs segregating within or between the two hybridizing species. SVs and SNPs exhibited similar levels of genetic differentiation between species, with the exception of inversions, which were more differentiated. We detected credible variation in patterns of introgression among SV loci in the hybrid zone, with 562 of 1419 ancestry-informative SVs exhibiting genomic clines that deviating from null expectations based on genome-average ancestry. Overall, hybrids exhibited a directional shift towards Jackson Hole Lycaeides ancestry at SV loci, consistent with the hypothesis that these loci experienced more selection on average then SNP loci. Surprisingly, we found that deletions, rather than inversions, showed the highest skew towards excess introgression from Jackson Hole Lycaeides. Excess Jackson Hole Lycaeides ancestry in hybrids was also especially pronounced for Z-linked SVs and inversions containing many genes. In conclusion, our results show that SVs are ubiquitous and suggest that SVs in general, but especially deletions, might contribute disproportionately to hybrid fitness and thus (partial) reproductive isolation.