Clay minerals can hinder the transport of various contaminants in soil and aquifer, but how clay minerals affect the transport of nanoparticles in aquifers has not been investigated in depth. In this paper, the transport of surfactants dispersed multi-walled carbon nanotubes (MWCNTs) in well-defined quartz sand and mixtures of quartz sand and clay minerals (kaolinite and montmorillonite) with varying ionic strengths was studied. Sodium dodecyl benzenesulfonate (SDBS) and octyl-phenol-ethoxylate (TX100) MWCNT suspensions can migrate through quartz sand easily, but the presence of less than 2% w/w clay minerals in quartz sand can significantly hinder the transport of MWCNT suspensions, especially at high ion strength (0.6 mM CaCl2). The inhibition mechanism of clay minerals for surfactant-dispersed MWCNTs in porous media is the interception of MWCNTs. Kaolinite has stronger inhibition effect for MWCNTs transport than montmorillonite because more kaolinite can be retained in the quartz sand. Adsorption of surfactants by clay minerals does not affect the transport of MWCNTs significantly. This finding is important for the environmental assessment of MWCNT transport risks in soils and aquifers.