Kendall shape spaces provide a powerful geometric framework for modeling shapes independently of rotation, translation, and scale. These spaces, which arise naturally in statistical shape analysis and morphometrics, are structured as quotient Riemannian manifolds, such as complex projective spaces. In parallel, quantum machine learning (QML) has shown promise in tackling high-dimensional data and structured learning problems, yet its extension to non-Euclidean data domains remains largely unexplored. In this work, we propose a theoretical framework that enables QML algorithms to operate on Kendall shape spaces. We define a quantum encoding scheme that maps centered and normalized shape configurations into quantum states via amplitude encoding on the complex projective manifold. Furthermore, we introduce a quantum kernel function grounded in the geodesic distance between shapes, enabling quantum-enhanced classification and clustering algorithms. This approach opens the door to geometric quantum learning on structured manifolds and offers new perspectives for the efficient quantum processing of shape-based data. We discuss the feasibility of implementing this framework on NISQ hardware and highlight its potential for future applications in quantum shape analysis and beyond.