The aim of this paper is to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces. These symmetric spaces are obtained as follows. We consider a graded simple real Lie algebra $widetilde{mathfrak g}$ of the form $widetilde{mathfrak g}=V^-oplus mathfrak goplus V^+$, where $[mathfrak g,V^+]subset V^+$, $[mathfrak g,V^-]subset V^-$ and $[V^-,V^+]subset mathfrak g$. If the graded algebra is regular, then a suitable group $G$ with Lie algebra $mathfrak g$ has a finite number of open orbits in $V^+$, each of them is a realization of a symmetric space $Gslash H_p$.The functional equation gives a matrix relation between the local zeta functions associated to $H_p$-invariant distributions vectors for the same minimal spherical representation of $G$. This is a generalization of the functional equation obtained by Godement} and Jacquet for the local zeta function attached to a coefficient of a representation of $GL(n,mathbb R)$.