You may be misleading yourself because hydrolysis means "to split with water", but in this reaction there is no water present, so it can not be a hydrolysis reaction. However, the reaction is still similar to hydrolysis but since the reactants are slightly different, the products will be slightly different. Think of how water and MeOH are different, but also how they are similar.
Since you seem to be familiar with the basic hydrolysis of water: how is the nucleophile that attacks the ester generated when the solvent is water (what's the acid and what's the base)? Now, what happens if instead of water, you substitute MeOH? What nucleophile gets generated? Run through the reaction mechanism with that nucleophile and see what comes out the other side.