Webber made contact with Vergne when trying to pass the Frenchman for 12th position on lap 16 of the race. He confirmed his penalty to reporters as he left the stewards' office.
The Australian said afterwards he was sure Vergne had left him room to pass, although the Toro Rosso driver denied knowing Webber was there.
"I think Mark could not have got through from where he tried and I'm not even sure if he was trying to pass me. Certainly I didn't even know he was there," said Vergne.
"Unfortunately, the impact put me into a spin and the incident damaged my floor. From then I lost a lot of downforce."
Webber had already endured a nightmare weekend.
The Australian had started the race from the pits after he had been excluded from qualifying for not having enough fuel in his car for scrutineering checks.
The Red Bull driver retired from the race after losing the rear left wheel following a pitstop.