This paper aims to study isometries of the 1-Wasserstein space \(\mathcal {W}_1(\textbf{G})\) over Carnot groups endowed with horizontally strictly convex norms. Well-known examples of horizontally strictly convex norms on Carnot groups are the Heisenberg group \(\mathbb {H}^n\) endowed with the Heisenberg-Korányi norm, or with the Naor-Lee norm; and H-type Iwasawa groups endowed with a Korányi-type norm. We prove that on a general Carnot group there always exists a horizontally strictly convex norm. The main result of the paper says that if \((\textbf{G},N_{\textbf{G}})\) is a Carnot group where \(N_{\textbf{G}}\) is a horizontally strictly convex norm on \(\textbf{G}\) , then the Wasserstein space \(\mathcal {W}_1(\textbf{G})\) is isometrically rigid. That is, for every isometry \(\Phi :\mathcal {W}_1(\textbf{G})\rightarrow \mathcal {W}_1(\textbf{G})\) there exists an isometry \(\psi :\textbf{G}\rightarrow \textbf{G}\) such that \(\Phi =\psi _{\#}\) .
