In blood samples from patients with viral infection, it is often important to separate viral particles from human cells, for example, to minimize background in performing viral whole genome sequencing. Here, we present a microfluidic device that uses spiral inertial microfluidics with continuous circulation to separate host cells from viral particles and free nucleic acid. We demonstrate that this device effectively reduces white blood cells, red blood cells, and platelets from both whole blood and plasma samples with excellent recovery of viral nucleic acid. Furthermore, microfluidic separation leads to greater viral genome coverage and depth, highlighting an important application of this device in processing clinical samples for viral genome sequencing.