The closest thing to what you're describing is the ability Mummy, which replaces the ability of any Pokémon that makes contact with it with Mummy. And then there's the situational fringe case of Aura Break, which reverses the effects of Dark Aura and Fairy Aura, but only those abilities. As of USUM, there are no Abilities that automatically suppress the opponent's ability when sent into battle, except for Aura Break in some cases.
Source: looked through every ability on this page.