Intracellular peptides (InPeps) generated by proteasomes were previously suggested as putative natural regulators of protein–protein interactions (PPI). Here, the main aim was to investigate the intracellular effects of intracellular peptide VFDVELL (VFD7) and related peptides on PPI. The internalization of the peptides was achieved using a C-terminus covalently bound cell-penetrating peptide (cpp; YGRKKRRQRRR). The possible inhibition of PPI was investigated using a NanoBiT® luciferase structural complementation reporter system, with a pair of plasmids vectors each encoding, simultaneously, either FK506-binding protein (FKBP) or FKBP-binding domain (FRB) of mechanistic target of rapamycin complex 1 (mTORC1). The interaction of FKBP–FRB within cells occurs under rapamycin induction. Results shown that rapamycin-induced interaction between FKBP–FRB within human embryonic kidney 293 (HEK293) cells was inhibited by VFD7-cpp (10–500 nM) and FDVELLYGRKKRRQRRR (VFD6-cpp; 1–500 nM); additional VFD7-cpp derivatives were either less or not effective in inhibiting FKBP–FRB interaction induced by rapamycin. Molecular dynamics simulations suggested that selected peptides, such as VFD7-cpp, VFD6-cpp, VFAVELLYGRKKKRRQRRR (VFA7-cpp), and VFEVELLYGRKKKRRQRRR (VFA7-cpp), bind to FKBP and to FRB protein surfaces. However, only VFD7-cpp and VFD6-cpp induced changes on FKBP structure, which could help with understanding their mechanism of PPI inhibition. InPeps extracted from HEK293 cells were found mainly associated with macromolecular components (i.e., proteins and/or nucleic acids), contributing to understanding InPeps’ intracellular proteolytic stability and mechanism of action-inhibiting PPI within cells. In a model of cell death induced by hypoxia-reoxygenation, VFD6-cpp (1 µM) increased the viability of mouse embryonic fibroblasts cells (MEF) expressing mTORC1-regulated autophagy-related gene 5 (Atg5), but not in autophagy-deficient MEF cells lacking the expression of Atg5. These data suggest that VFD6-cpp could have therapeutic applications reducing undesired side effects of rapamycin long-term treatments. In summary, the present report provides further evidence that InPeps have biological significance and could be valuable tools for the rational design of therapeutic molecules targeting intracellular PPI.