Synthesis of graphene (GN) in 2004 stimulated wide interest in potential applications of 2D materials in catalysis, optoelectronics, biotechnology, and construction of sensing devices. In the presented study, interactions between GN sheets and phospholipid bilayers are examined using steered molecular dynamics simulations. GN sheets of different sizes were inserted into a bilayer and subsequently withdrawn from it at two different rates (1 and 2 m/s). In some cases, nanoindentation led to substantial damage of the phospholipid bilayer; however, an effective self-sealing process occurred even after significant degradation. The average force and work, deflection of the membrane during indentation, withdrawal processes, and structural changes caused by moving sheets are discussed. These quantities are utilized to estimate the suitability of GN sheets for targeted drug delivery or other nanomedicine tools. The results are compared with those obtained for other nanostructures such as homogeneous and heterogeneous nanotubes.