Asphalt pavement cracks not only reduce road life and affect traffic safety but also increase maintenance costs. These issues can be solved significantly if microwave heating (MH) technology is applied based on the self-healing mechanism. This work aims to adopt carbon nanotubes (CNTs) to modify asphalt binders to accelerate their self-healing properties. Thermal conductivity and diffusivity, high-temperature rheological characteristics, and fatigue resistance were conducted to investigate healing potential from binders level; semicircular bending (SCB) tests and MH test were used to assess the fracture and self-healing properties from mix level; Grey relational analysis (GRA) was employed to study the relevance of asphalt binder properties on the healing properties of mixes. Results indicated that CNTs could improve asphalt binders' thermal conductivity, thermal diffusivity, high-temperature deformation resistance, and anti-fatigue properties. However, the J_nr-diff results suggest that the content of CNTs needs to be controlled within 1.0%. From the mixtures perspective, samples with 1.0% content of CNTs can achieve the best fracture performance and healing efficiency with excellent heating uniformity and no overheating problems. Furthermore, thermal performance strongly correlates with mixtures' healing indexes. This research addresses the maintenance of asphalt pavement cracks, which is essential for long-life pavements and sustainable road development.