Let $ \mathcal{M} $ be a Hilbert C$ ^* $-module. A sequence of linear mappings $ \{\varphi_n : \mathcal{M} \rightarrow \mathcal{M} \}_{n=0}^{+\infty}$ with $ \varphi_0=I $, is said to be a Hilbert C$ ^* $-module Jordan higher derivation on $ \mathcal{M} $, if it satisfies the equation \begin{equation*} ǎrphi_n (⟨a,b ⟩a) =um_{i+j+k=n}⟨ǎrphi_i (a),ǎrphi_j(b)⟩ǎrphi_k(a), \end{equation*} for all $ a,b \in \mathcal{M} $ and each non-negative integer $ n $. In this paper, we show that, if $ \mathcal{M} $ is prime, then every Hilbert C$ ^* $-module Jordan higher derivation $ \{\varphi_n\}_{n=0}^{+\infty} $ on $ \mathcal{M} $, is a Hilbert C$ ^* $-module higher derivation on $ \mathcal{M} $. As a consequence, we show that every Hilbert C$ ^* $-module Jordan derivation on $ \mathcal{M} $, is a Hilbert C$ ^* $-module derivation on $ \mathcal{M} $.