Max Verstappen has been promoted.
Red Bull announced on their official website this morning that Kvyat has been moved to sister team Toro Rosso - a demotion, with Max Verstappen taking his place.
McLaren driver Button commented on Twitter, accusing Red Bull of being too reactive, and having short memories.
Red Bull team principal Christian Horner explained the switch: "Max has proven to be an outstanding young talent. His performance at Toro Rosso has been impressive so far and we are pleased to give him the opportunity to drive for Red Bull Racing.
"We are in the unique position to have all four drivers across Red Bull Racing and Toro Rosso under long term contracts with Red Bull, so we have the flexibility to move them between the two teams.
"Dany will be able to continue his development at Toro Rosso, in a team that he is familiar with, giving him the chance to regain his form and show his potential."
So far this season Kvyat has amassed 21 points, ninth in the driver standings, behind teammate Daniel Ricciardo, who is in fourth with 36.
Verstappen, in the inferior Toro Rosso, has 13 points. Leader Nico Rosberg of Mercedes has 100 points.