Explosive developments in mRNA vaccine technology in the last decade have made it possible to achieve great success in clinical trials of mRNA vaccines to prevent infectious diseases and develop cancer treatments and mRNA-based gene therapy products. The approval of the mRNA-1273 and BNT162b2 mRNA vaccines against SARS-CoV-2 by the U.S. Food and Drug Administration has led to mass vaccination (with mRNA vaccines) of several hundred million people around the world, including children. Despite its effectiveness in the fight against COVID-19, rare adverse effects of the vaccination have been shown in some studies, including vascular microcirculation disorders and autoimmune and allergic reactions. The biodistribution of mRNA vaccines remains one of the most poorly investigated topics. This mini-review discussed the results of recent experimental studies on humans and rodents regarding the biodistribution of mRNA vaccines, their constituents (mRNA and lipid nanoparticles), and their encoded antigens. We focused on the dynamics of the biodistribution of mRNA vaccine products and on the possibility of crossing the blood-brain and blood-placental barriers as well as transmission to infants through breast milk. In addition, we critically assessed the strengths and weaknesses of the detection methods that have been applied in these articles, whose results' reliability is becoming a subject of debate.