The Future Circular Collider for hadrons (FCC-hh) is the proposed high-energy frontier particle collider, which is expected to enable proton-proton collisions at a center-of-mass energy of 100 TeV. The specifications for the FCC-hh injection kicker system are very challenging. To provide fast magnetic field rise and fall times, and low ripple during the flat-top, ferrite loaded transmission line type magnets will be used. To limit the beam coupling impedance, a suitable beam screen will be placed in the aperture of each kicker magnet. Due to issues associated with the "conventional" beam screen design, used in the injection kickers magnets of the Large Hadron Collider (LHC), such as high voltage (HV) breakdowns and yoke heating problems, we have developed a novel concept of a helical beam screen. The fundamental advantage of the new design, in comparison to the conventional beam screen, is a significant reduction of the maximum voltage induced on the screen conductors, thus a greatly reduced probability of an electrical breakdown of the beam screen. In addition, the longitudinal beam coupling impedance of the helical beam screen is optimized to reduce power deposition in the kicker magnet. Furthermore, the helical beam screen allows a reduction of the maximum transverse beam coupling impedance of the kicker system. Detailed numerical simulations, theoretical studies and experimental results demonstrate that a new design is a promising solution not only for the FCC-hh, but also for existing machines.