Vergne initially qualified 11th for Sunday's race at Suzuka, but has been penalised after he was forced to make an engine change ahead of the session.
Formula One regulations for 2014 prohibit teams from using more than five of any of the six power unit components over the course of a season.
Vergne will now start from the back row, together with Pastor Maldonado, who was handed the same 10-place punishment prior to qualifying 17th.
Daniil Kvyat, Vergne's team-mate who is to join Red Bull next season as the replacement for Sebastian Vettel, was the first man to use a sixth engine this season and received a grid drop at Monza last month.
Toro Rosso's deputy technical director Ben Waterhouse said of Vergne's penalty: "The most important thing is that he managed to qualify above P12 and so he takes all his penalty here, with none of it carried over to Russia next weekend."