  We show that if $ \mathcal{Z} $ is a dp-minimal expansion of $
\left(\mathbb{Z},+,0,1\right) $ that defines an infinite subset of $ \mathbb{N}
$, then $ \mathcal{Z} $ is interdefinable with $ \left(\mathbb{Z},+,0,1, <
\right) $. As a corollary, we show the same for dp-minimal expansions of $
\left(\mathbb{Z},+,0,1\right) $ which do not eliminate $ \exists^{\infty} $.
