This work belongs to the development of mechanical force-responsive drug delivery systems based on remote stimulation by an external magnetic field at the first stage, assisting the positioning of a ferrogel-based targeted delivery platform in a fluid flow. Magnetically active biopolymer beads were considered a prototype implant for the needs of replacement therapy and regenerative medicine. Spherical calcium alginate ferrogels (FGs)~2.4 mm in diameter, filled with a 12.6% weight fraction of magnetite particles of 200–300 nm in diameter, were synthesized. A detailed characterization of the physicochemical and magnetic properties of FGs was carried out, as were direct measurements of the field dependence of the attractive force for FG-beads. The hydrodynamic effects of the positioning of FG-beads in a fluid flow by a magnetic field were studied experimentally in a model vessel with a fluid stream. Experimental results were compared with the results of mathematical and computer modeling, showing reasonable agreement. The contributions of the hydrodynamic and magnetic forces acting on the FG-bead in a fluid flow were discussed. Obtained forces for a single ferrogel implant were as high as 0 to 10−4 N for the external field range of 0 to 35 kA/m, perfectly in the range of mechanical force stimuli in biological systems.