An apparatus for manufacturing a carbon nanostructure and a method for manufacturing a carbon nanostructure that can achieve an increase in length and shape stabilization of the carbon nanostructure can be obtained. A manufacturing apparatus for a carbon nanostructure includes a catalyst member on which a carbon nanostructure is grown, a source gas supply unit and a source gas supply pipe, a coil, and a heater. The source gas supply unit and the source gas supply pipe supply the catalyst member with carbon for forming the carbon nanotube. The coil applies a gradient magnetic field (e.g., a cusped magnetic field indicated by magnetic flux line whose magnetic field strength gradually increases from one surface of the catalyst member to the other surface opposite to the one surface. The heater heats the catalyst member.