Human phonation involves the flow-induced vibrations of the vocal folds (VFs) that result from the interaction with airflow through the larynx. Most voice dysfunctions correspond with the fluid–structure interaction (FSI) features as well as the local changes in perfusion within the VF tissue. This study aims to develop a multiphysics computational framework to simulate the interstitial fluid flow dynamics in vibrating VFs using a biphasic description of the tissue and FSI methodology. The integration of FSI and a permeable VF model presents a novel approach to capture phonation physics' complexity and investigate VF tissue's porous nature. The glottal airflow is modeled by the unsteady, incompressible Navier–Stokes equations, and the Brinkman equation is employed to simulate the flow through the saturated porous medium of the VFs. The computational model provides a prediction of tissue deformation metrics and pulsatile glottal flow, in addition to the interstitial fluid velocity and flow circulation within the porous structure. Furthermore, the model is used to characterize the effects of variation in subglottal lung pressure and VF permeability coefficient by conducting parametric studies. Subsequent investigations to quantify the relationships between these input variables, flow perfusion, pore pressure, and vibration amplitude are presented. A linear relationship is found between the vibration amplitude, pore pressure, and filtration flow with subglottal pressure, whereas a nonlinear dependence between the filtration velocity and VF permeability coefficient is detected. The outcomes highlight the importance of poroelasticity in phonation models.