Coronaviruses, especially severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), present an ongoing threat to human wellbeing. Consequently, elucidation of molecular determinants of their function and interaction with the host is an important task. Whereas some of the coronaviral proteins are extensively characterized, others remain understudied. Here, we use molecular dynamics simulations to analyze the structure and dynamics of the SARS-CoV-2 envelope (E) protein (a viroporin) in the monomeric form. The protein consists of the hydrophobic α-helical transmembrane domain (TMD) and amphiphilic α-helices H2 and H3, connected by flexible linkers. We show that TMD has a preferable orientation in the membrane, while H2 and H3 reside at the membrane surface. Orientation of H2 is strongly influenced by palmitoylation of cysteines Cys40, Cys43, and Cys44. Glycosylation of Asn66 affects the orientation of H3. We also observe that the monomeric E protein both generates and senses the membrane curvature, preferably localizing with the C-terminus at the convex regions of the membrane; the protein in the pentameric form displays these properties as well. Localization to curved regions may be favorable for assembly of the E protein oligomers, whereas induction of curvature may facilitate the budding of the viral particles. The presented results may be helpful for a better understanding of the function of the coronaviral E protein and viroporins in general, and for overcoming the ongoing SARS-CoV-2 pandemic.