Common salvinia, Salvinia minima Baker (Salviniaceae), is a small, floating aquatic fern native to Central and South America that has invaded fresh water bodies in southeastern United States since the 1930s. We examined genetic variation across much of the introduced range of this species in the United States using codominant RAD-seq markers. Data from over 600 variable loci showed a reduction in heterozygosity from east to west in addition to a corresponding trend in assignment of samples to one of two genetic groups. Our data are consistent with previous published work and with the hypothesis that common salvinia had a single introduction on the east end of its current range in the United States. From there it migrated westward, losing genetic diversity during this spread. The data are also consistent with sexual reproduction, although we are unable to estimate the extent of this relative to asexual spreading. Future genetic work should include sampling from the native range to help determine the original sources of North American common salvinia.