Electrochemical sensors have found a wide range of applications in analytical chemistry thanks to the advent of high-throughput printing technologies. However, these techniques are usually limited to two-dimensional (2D) geometry with relatively large minimal feature sizes. Here, we report on the scalable fabrication of monolithically integrated electrochemical devices with novel and customizable fiber-based architectures. The multimaterial thermal drawing technique is employed to co-process polymer composites and metallic glass into uniform electroactive and pseudoreference electrodes embedded in an insulating polymer cladding fiber. To demonstrate the versatility of the process, we tailor the fiber microstructure to two configurations: a small-footprint fiber tip sensor and a high-surface-area capillary cell. We demonstrate the performance of our devices using cyclic voltammetry and chronoamperometry for the direct detection and quantification of paracetamol, a common anesthetic drug. Finally, we showcase a fully portable pipet-based analyzer using low-power electronics and an "electrochemical pipet tip" for direct sampling and analysis of microliter-range volumes. Our approach paves the way toward novel materials and architectures for efficient electrochemical sensing to be deployed in existing and novel personal care and surgical configurations.