To provide a fiber dyed yarn having moderate stretch characteristics and an excellent touch feeling and appearance quality.

The polyester fiber dyed yarn is composed of a side-by-side type or an eccentric sheath-core type conjugated polyester conjugated fiber in which at least one layer is layer consisting essentially of polytrimethylene terephthalate and has 20-50% elastic recovery ratio at 10% stretch and ≤4% shrinkage percentage in boiling water. The polyester fiber dyed yarn is produced by subjecting a filament yarn composed of the side-by-side type or eccentric sheath-core type conjugated polyester conjugated fiber of the polytrimethylene terephthalate and polyethylene terephthalate to a tensioning treatment, carrying out relaxing heat treatment, then performing cheese winding and subjecting the resultant cheese to cheese dyeing.