Although COVID-19 is primarily a respiratory disease, it may affect also the cardiovascular system. COVID-19 patients with cardiovascular disorder (CVD) develop a more severe disease course with a significantly higher mortality rate than non-CVD patients. A common denominator of CVD is the dysfunction of endothelial cells (ECs), increased vascular permeability, endothelial-to-mesenchymal transition, coagulation, and inflammation. It has been assumed that clinical complications in COVID-19 patients suffering from CVD are caused by SARS-CoV-2 infection of ECs through the angiotensin-converting enzyme 2 (ACE2) receptor and the cellular transmembrane protease serine 2 (TMPRSS2) and the consequent dysfunction of the infected vascular cells. Meanwhile, other factors associated with SARS-CoV-2 entry into the host cells have been described, including disintegrin and metalloproteinase domain-containing protein 17 (ADAM17), the C-type lectin CD209L or heparan sulfate proteoglycans (HSPG). Here, we discuss the current data about the putative entry of SARS-CoV-2 into endothelial and smooth muscle cells. Furthermore, we highlight the potential role of long non-coding RNAs (lncRNAs) affecting vascular permeability in CVD, a process that might exacerbate disease in COVID-19 patients.