This work reports an experimental study of the kinetics and mechanisms of gelation of carbon nanotubes (CNTs)-hyaluronic acid (HA) mixtures. These materials are of great interest as functional biogels for future medical applications and tissue engineering. We show that CNTs can induce the gelation of noncovalently modified HA in water. This gelation is associated with a dynamical arrest of a liquid crystal phase separation, as shown by small-angle light scattering and polarized optical microscopy. This phenomenon is reminiscent of arrested phase separations in other colloidal systems in the presence of attractive interactions. The gelation time is found to strongly vary with the concentrations of both HA and CNTs. Near-infrared photoluminescence reveals that the CNTs remain individualized both in fluid and in gel states. It is concluded that the attractive forces interplay are likely weak depletion interactions and not strong van der Waals interactions which could promote CNT rebundling, as observed in other biopolymer-CNT mixtures. The present results clarify the remarkable efficiency of CNT at inducing the gelation of HA, by considering that CNTs easily phase separate as liquid crystals because of their giant aspect ratio.