VRC01 is a broadly neutralizing antibody that targets the CD4 binding site of HIV-1 gp120. Passive administration of VRC01 in humans has assessed the safety and the effect on plasma viremia of this monoclonal antibody (mAb) in a phase 1 clinical trial. After VRC01 infusion, the plasma viral load in most of the participants was reduced but had particular dynamics not observed during antiretroviral therapy. In this paper, we introduce different mathematical models to explain the observed dynamics and fit them to the plasma viral load data. Based on the fitting results we argue that a model containing reversible Ab binding to virions and clearance of virus-VRC01 complexes by a two-step process that includes (1) saturable capture followed by (2) internalization/degradation by phagocytes, best explains the data. This model predicts that VRC01 may enhance the clearance of Ab-virus complexes, explaining the initial viral decay observed immediately after antibody infusion in some participants. Because Ab-virus complexes are assumed to be unable to infect cells, i.e., contain neutralized virus, the model predicts a longer-term viral decay consistent with that observed in the VRC01 treated participants. By assuming a homogeneous viral population sensitive to VRC01, the model provides good fits to all of the participant data. However, the fits are improved by assuming that there were two populations of virus, one more susceptible to antibody-mediated neutralization than the other.