Ferrari boss Maurizio Arrivabene has hit back with fury at Mercedes, after an accusation of deliberate foul play at Silverstone.
Sebastian Vettel, who re-takes the championship lead after winning at Silverstone, called the accusations of deliberate Ferrari sabotage "silly".
Meanwhile, Wolff's counterpart at Ferrari, Arrivabene, was livid.
"Who is incompetent? Kimi? Who is he to judge what the drivers are doing in the car? If he really said something like that, he should be ashamed," he told Sky Italia.
"Allison worked at Maranello for many years, but now we are here in England teaching him to be a gentleman.
"I accept it from Jacques Villeneuve because he was a driver. But this guy?"
Red Bull's Christian Horner said it is obvious that "tension" between the top two teams is hotting up at the mid-point of an intense championship fight.
"When you have that growing tension, speculation is unavoidable when these incidents occur," he said.
"But I believe it's nothing more than a racing incident. I would be surprised if there was anything else or if Kimi is that kind of driver."
Mercedes's Valtteri Bottas also played down the incident and the accusations.
"We are always racing closely with Ferrari and there can always be contact," he said.
However, Mercedes team chairman Niki Lauda commented: "The accident was just unfair. It was the second time a Ferrari has hit us in the first corner. That's not funny."
The championship continues next weekend with the German Grand Prix.