Copper(II)-terpyridine complexes are endowed with the ability to generate reactive oxygen species (ROS) and induce cancer cell death. Here we report the synthesis, characterisation, and anti-breast cancer stem cell (CSC) properties of a series of copper(II)-terpyridine complexes containing aryl sulfonamide groups (1–5). All of the copper(II)-terpyridine complexes adopt distorted square pyramidal geometries and are suitably stable in biologically relevant solutions (PBS and cell culture media). The p-toluene sulfonamide-bearing copper(II)-terpyridine complex 1 is 6–8-fold more potent towards breast CSCs than salinomycin (an established anti-CSC agent) and cisplatin (a metal-based anticancer drug). The copper(II)-terpyridine complex 1 also reduces the formation, size, and viability of three-dimensionally cultured mammospheres, to a similar or better extent than salinomycin and cisplatin. Mechanistic studies show that 1 successfully enters breast CSCs, generates intracellular ROS at short exposure times, partially induces endoplasmic reticulum stress, and triggers apoptosis. To the best of our knowledge, this is the first study to investigate the anti-breast CSC properties of copper(II)-terpyridine complexes.