  We define, for each quasi-syntomic ring $R$ (in the sense of
Bhatt-Morrow-Scholze), a category $\mathrm{DM}^{\rm adm}(R)$ of
\textit{admissible prismatic Dieudonn\'e crystals over $R$} and a natural
functor from $p$-divisible groups over $R$ to $\mathrm{DM}^{\rm adm}(R)$. We
prove that this functor is an antiequivalence. Our main cohomological tool is
the prismatic formalism recently developed by Bhatt and Scholze.
