Let $\Lambda$ be a preprojective algebra of type $A,D,E$, and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $\mathrm{Sub}Q$ for $Q$ an injective $\Lambda$-module, and we introduce a mutation operation between complete rigid modules in $\mathrm{Sub}Q$. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$.