Living ceramic materials are proposed as high-performance engineered living materials due to their expected properties, including improved mechanical stability and performance, which could impact a wide range of applications across various fields. Particularly, living ceramic fibers are anticipated to exhibit even superior mechanical and structural properties, considering their fibril nature. This work presents the foundation for developing the family of living ceramic fibers. Ureolytic bacteria, Sporosarcina pasteurii, are encapsulated within electrospun alginate fibers, which are further subjected to biomineralization. A live-dead assay reveals that the encapsulated bacteria survive the electrospinning process. Successful biomineralization of the fibers results in the precipitation of near-spherical calcium carbonate nanoparticles at the fiber sites. The cell density within the fibers exhibits a significant impact on the packing of calcium carbonate nanoparticles. While further extensive research is required to fully realize the potential of living ceramic fibers, the findings of this study represent a significant step toward their development.