The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper we derive the Vertex and Edge Connectivity of the zero divisor graph $Γ[\mathbb{Z}_n]$, for any natural number $n$ . We also discuss the minimum degree of the zero divisor graph $Γ[\mathbb{Z}_n]$.