A toolholder includes a cutting tool mounted to a head attached to a collar at a first end of the toolholder. A shank is located at a second, opposite end of the toolholder. A central cavity extends inwardly from the first end toward the shank. A viscous fluid inertia mass damper is disposed within the central cavity. The viscous fluid inertia mass damper includes an absorber body having a first end, a second end opposite the first end, a fluid reservoir formed in the damper body for containing a viscous fluid, and a plurality of apertures formed in the damper body for allowing the viscous fluid to flow from the fluid reservoir and through the apertures to suppress vibration of the toolholder. A method for suppressing vibrations in a toolholder is also disclosed.