We present a mechanism in the field of microfluidics by which the stratification of a viscoelastic fluid can be induced in a channel on the microscale by applying a dynamic pressure gradient at frequencies within the range of sound. Stratification is obtained with identical layers, parallel to the channel walls, whose number can be tailored. These layers are separated by 2D zero-velocity planes. This would allow different tracer particles with small diffusion coefficients to be confined in different fluid layers within the same microchannel. We obtain analytical results that allow us to make theoretical predictions regarding the possible experimental realization of stratification in a microchannel using a biofluid. We find a relation among the diffusion coefficient, fluid properties, and microchannel thickness that establishes a condition for the confinement of tracer particles to a layer. This mechanism has potential use in micrototal analysis systems and MEMS-containing viscoelastic fluids.