It is known that a harmonic minimal graph in 3-dimensional Euclidean space is locally either a plane or a helicoid. We prove that any harmonic minimal graph in \({{\mathbb {R}}}^{n+1}\) is locally foliated by \((n-1)\) -dimensional minimal graphs. Moreover, it is proved that a harmonic minimal graph in \(M^{2}\times {{\mathbb {R}}}\) is locally either a horizontal level surface or a helicoid, where \(M^2\) denotes either 2-dimensional hyperbolic space \({\mathbb {H}}^2\) or the 2-dimensional unit sphere \({\mathbb {S}}^{2}\) .
