The process of assembling particles into organized functional structures is influenced by the rheological properties of the matrix fluid in which the assembly takes place. Therefore, tuning these I properties represents a viable and as yet unexplored approach for controlling particle assembly. In this Letter, we examine the effect of the matrix fluid yield stress on the directed assembly of polarizable particles into linear chains under a uniform external magnetic field. Using particle-level simulations with a simple yield stress model, we find that chain growth follows the same trajectory as in Newtonian matrix fluids up to a critical time that depends on the balance between the yield stress and the strength of magnetic interactions between particles; subsequently, the system undergoes structural arrest. Appropriate dimensionless groups for characterizing the arresting behavior are determined and relationships between these groups and the resulting structural properties are presented. Since field-induced structures can be indefinitely stabilized by the matrix fluid yield stress and "frozen" into place as desired, this approach may facilitate the assembly of more complex and sophisticated structures.