Understanding thermal transport through nanoscale van der Waals interfaces is vital for addressing thermal management challenges in nanoelectronic devices such as those made of assembled nanostructure arrays; however, the interfacial thermal conductance (GCA) remains poorly characterized because of technical challenges. In this work, we present an experimental approach and an interface heat transfer model to determine the GCA between two individual copper phthalocyanine (CuPc) nanoribbons. The GCA is found to be on the order of 105 Wm−2K−1 at 300 K, which is more than two orders of magnitude lower than the value predicted by molecular dynamics (MD) simulations for a perfectly smooth interface between two parallelly aligned CuPc nanoribbons. Further MD simulations and contact mechanics analysis reveal that surface roughness can significantly reduce the adhesion energy and the effective contact area between CuPc nanoribbons and thus result in an ultralow GCA. In addition, the adhesion energy at the interface also depends on the stacking configuration of two CuPc nanoribbons, which also contributes to the observed ultralow GCA. This work provides a new approach for studying thermal transport through nanoscale van der Waals interfaces and discloses the critical role of nanoscale surface roughness in reducing the GCA.