For any graph $G$, a subset $S\subseteq V(G)$ is said to be a cycle isolating set of $G$ if $G-N[S]$ contains no cycle, where $N[S]$ is the closed neighborhood of $S$. The cycle isolation number of $G$, denoted by $\iota_c(G)$, is the minimum cardinality of a cycle isolating set of $G$. Borg (2020) showed that if $G$ is a connected $n$-vertex graph that is not isomorphic to $C_3$, then $\iota_c(G)\leq \frac{n}{4}$. We present a sharp upper bound on the cycle isolation number of a connected graph in terms of its number of edges. We prove that if $G$ is a connected $m$-edge graph that is not isomorphic to $C_3$, then $\iota_c(G)\leq \frac{m+1}{5}$. Moreover, we characterize all connected graphs attaining this bound.