The Cuban solenodon (Solenodon cubanus) is one of the most enigmatic mammals and is an extremely rare species with a distribution limited to a small part of the island of Cuba. Despite its rarity, in 2012 seven individuals of S. cubanus were captured and sampled successfully for DNA analysis, providing new insights into the evolutionary origin of this species and into the origins of the Caribbean fauna, which remain controversial. We conducted molecular phylogenetic analyses of five nuclear genes (Apob, Atp7a, Bdnf, Brca1 and Rag1; total, 4,602 bp) from 35 species of the mammalian order Eulipotyphla. Based on Bayesian relaxed molecular clock analyses, the family Solenodontidae diverged from other eulipotyphlan in the Paleocene, after the bolide impact on the Yucatan Peninsula, and S. cubanus diverged from the Hispaniolan solenodon (S. paradoxus) in the Early Pliocene. The strikingly recent divergence time estimates suggest that S. cubanus and its ancestral lineage originated via over-water dispersal rather than vicariance events, as had previously been hypothesised.