The present investigation is connected to the field of medical textiles, which includes the development and application of composite fibers. The aim of the paper is the processing and investigation of polyamide 6 (PA6)–amber composite fibers. The use of amber filler for the preparation of a new type of polymer composite fiber is described in detail for the first time. Scanning electron microscopy (SEM), atomic force microscopy (AFM) and granulometry testing were used to test the structure and the size of the prepared amber particles. The obtained amber particles were characterized by an average size of up to 3 mm and a regular shape. Fourier transform infrared (FTIR) spectroscopy investigations showed that amber in the dispersed state does not change its chemical structure and contains one of the active compounds— succinic acid. The effect of the amber filler inclusion on the melt-spinning routes of fully drawn yarns (FDY) and pre-oriented yarns (POY) was determined. Amber composite fibers general use is medical fabric (compression socks and tights); it is biocompatible with skin cells.