No, the Higgs mechanism does not directly result in the quantization of mass. The Higgs mechanism is responsible for giving elementary particles their mass by interacting with the Higgs field. The Higgs field permeates all of space, and particles acquire mass through their interactions with this field. However, the quantization of mass is a fundamental concept in quantum mechanics and is not specifically linked to the Higgs mechanism.
In quantum mechanics, particles and their associated properties, such as energy, momentum, and angular momentum, can only take on certain discrete values called quanta. This quantization arises from the wave-particle duality of quantum mechanics and is not directly related to the Higgs mechanism. The quantization of energy is described by Planck's constant, which sets the scale for these discrete energy levels.
So while the Higgs mechanism is responsible for the generation of particle masses, the quantization of mass is a broader concept in quantum mechanics that applies to all particles, irrespective of the Higgs mechanism.