For an abelian group $Γ$, a graph $G$ is said to be $Γ$-flow-critical if $G$ does not admit a nowhere-zero $Γ$-flow, but for each edge $e\in E(G)$, the contraction $G/e$ has a nowhere-zero $Γ$-flow. A bound on the density of $Z_3$-flow-critical graphs drawn on a fixed surface is obtained, generalizing the planar case of the bound on the density of 4-critical graphs by Kostochka and Yancey.