The study of drop deformation in response to variousstresses haslong piqued the interest of several academics. The deformation behaviorof cells, drug carriers, and even drug particles moving via microcapillariesinside the human body can be modeled using a viscoelastic drop model.A drop breakup study can also provide better design guidance for nanocarriersthat can deliver on-demand burst drug releases at specific cancersites. Thus, we attempted to investigate the deformation and breakupof a shear-thinning finitely extensible nonlinear elastic-peterlin(FENE-P) drop moving through the constricted microchannel. The computationalsimulation suggested that drop deformation and breakup can be manipulatedby varying of parameters like channel confinement, Deborah number,solvent viscosity ratio, viscosity ratio, and capillary number. Weattempted to find the critical capillary number for initiation ofdrop breakup. Observations from present study will give valuable insightsinto deformation and breakup patterns of drug carriers inside constrictedmicrocapillaries. The simulations of the two-phase viscoelastic drop Newtonianmatrix system were performed on an open-source solver, Basilisk.