Mechanical stimulation of bioprinted constructs can enhance the differentiation of cells within these scaffolds, such as driving chondrocytes towards cartilage tissue substitutes. In this study, a holistic approach is presented for designing and engineering a material-specific device based on a magnetic field setup using the Maxwell configuration for a touchless cyclic magnetic stimulation of (bioprinted) hydrogel scaffolds containing magnetic microparticles. We describe the entire development process, from the design of the magnetic field to the construction of the bioreactor and provide an evaluation of the calculation. Finally, an analysis of the distribution and orientation of the particles within the hydrogels and a cytocompatibility test after applying the intended stimulation regime were conducted. As a proof-of-principle, a model system in the shape of a cylindrical bending beam consisting of the established magnetisable bioink based on alginate, methylcellulose and magnetite microparticles (algMC + mag), was used instead of 3D printed, macroporous scaffolds of this material. Requirements for the dimensioning of the force, such as the Young's modulus, were determined experimentally. The magnetic field was calculated using the software Finite Element Method Magnetics (FEMM). The cyclic stimulation of the samples was performed over 14 days with a duration of 3 h per day. The aim was to achieve an elongation of up to 10%. The homogeneous particle distribution in stimulated and non-stimulated samples was proven via μCT and digital image processing (DIP). Even after applying a static magnetic field over 30 min, no structure formation such as chains or agglomeration of the magnetic particles were observed. The deformation behaviour defined as a shifted position of the neutral fibre (centre line of an object) during stimulation was measured via μCT and analysed using DIP. From these data, an elongation of approx. 9% was calculated for day 14. This elongation was achieved for both the stimulated samples and the control group without stimulation, which corresponds to the theoretically calculated value. The cytocompatibility of the bioink, scaffold environment and stimulation approach was demonstrated for bioprinted scaffolds with embedded human mesenchymal stem cells and chondrocytes. These findings proved the suitability and versatility of the bioreactor and the presented approach for stimulation experiments.