A three-dimensional breakdown behavior of the magnetic Bloch-point domain wall (BP-DW) propagation was investigated in a ferromagnetic nanowire with the variation of the external magnetic field by means of micromagnetic simulation. As magnetic field strength increases up to a threshold value, the BP-DW velocity approaches a critical phase velocity of the spontaneously emitting spin wave (SW), where a Cherenkov-type DW breakdown phenomenon is observed originating from an interaction between the spontaneously emitting SW and the BP-DW. It is found that the velocity of the BP-DW approaches a maximum value (∼2000 m/s) due to the intrinsic reversal time of a BP spin texture. This suggests that although cylindrical ferromagnetic nanowires might be free from the two-dimensional Walker breakdown phenomenon, there exists a Cherenkov-type three-dimensional breakdown behavior.