Electrochemical analysis based on screen-printed electrodes (SPEs) represents a great alternative to conventional analytical methods such as ICP-MS or LC-MS due to their portability, sensitivity, selectivity, and cost-effectiveness. In addition, the functionalization of SPEs with nanomaterials has been reported to provide an enhanced analytical performance. In this regard, silver nanoparticles (AgNPs) were synthesized and appropriately characterized, showing spherical silver nanoseeds (Ag-NS) with a diameter of 12.20 ± 0.04 nm. Using the drop-casting methodology, the synthesized AgNPs were used to modify screen-printed carbon nanofiber electrodes (SPCNFEs). Ag-NS deposition onto the electrode surface was confirmed by scanning electron microscopy (SEM). Furthermore, the analytical response of the modified electrodes (Ag-NS-SPCNFE) was evaluated for the determination of trace Pb(II), Cd(II), and As(V) using differential pulse anodic stripping voltammetry (DPASV), obtaining detection limits of 3.3, 3.7, and 2.6 µg L−1, for Pb(II), Cd(II) and As(V), respectively. Finally, Ag-NS-SPCNFE was tested towards the determination of As(V) in a spiked tap water sample, showing a good agreement with concentrations determined by ICP-MS.