In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a self-concordant barrier and whose underlying map has Lipschitz continuous derivative. The method performs two types of iterations, namely: those which follow an ever changing path within a certain ``proximal interior central surface'' and those which correspond to a "large-step" hybrid-proximal extragradient iteration. Due to its first-order nature, the iteration-complexity of the method is shown to be faster than its $0$-th order counterparts such as Korpelevich's algorithm and Tseng's modified forward-backward splitting method.