To provide a permanent magnet embedded rotor capable of reducing a torque ripple without reducing torque even if a gap is formed in a rotor core, and to provide a rotary electric machine incorporating the same.

The permanent magnet embedded rotor 15 has a first permanent magnet 17 embedded in the proximity of an outer peripheral surface 16b of a rotor core 16 to extend in a direction perpendicular to the d axis, and has second permanent magnets 18 embedded on the both sides of the first permanent magnet 17 so as to extend along the q axis. A second gap 22 is formed in the rotor core 16 apart from the both ends of the first permanent magnet 17 in the proximity of the q axis. The second gap 22 is composed with a base 221 located nearer the q axis than the first permanent magnet 17 is, and a gap extension part 222 that extends from the base 221 to the side of the d axis. The gap extension part 222 is configured such that its opening has narrower width than that of the opening of the base 221.