A microvalve‐based bioprinting system for the manufacturing of high‐resolution, multimaterial 3D‐structures is reported. Applying a straightforward fluid‐dynamics model, the shear stress at the nozzle site can precisely be controlled. Using this system, a broad study on how cell viability and proliferation potential are affected by different levels of shear stress is conducted. Complex, multimaterial 3D structures are printed with high resolution. This work pioneers the investigation of shear stress‐induced cell damage in 3D bioprinting and might help to comprehend and improve the outcome of cell‐printing studies in the future.