Animal model studies and first clinical trials have demonstrated the safety and efficacy of the mesenchymal stem cells’ (MSCs) transplantation in stroke. Intra-arterial (IA) administration looks especially promising, since it provides targeted cell delivery to the ischemic brain, is highly effective, and can be safe as long as the infusion is conducted appropriately. However, wider clinical application of the IA MSCs transplantation will only be possible after a better understanding of the mechanism of their therapeutic action is achieved. On the way to achieve this goal, the study of transplanted cells’ fate and their interactions with the blood–brain barrier (BBB) structures could be one of the key factors. In this review, we analyze the available data concerning one of the most important aspects of the transplanted MSCs’ action—the ability of cells to cross the blood–brain barrier (BBB) in vitro and in vivo after IA administration into animals with experimental stroke. The collected data show that some of the transplanted MSCs temporarily attach to the walls of the cerebral vessels and then return to the bloodstream or penetrate the BBB and either undergo homing in the perivascular space or penetrate deeper into the parenchyma. Transmigration across the BBB is not necessary for the induction of therapeutic effects, which can be incited through a paracrine mechanism even by cells located inside the blood vessels.