Esteban Gutierrez gets the same punishment for blocking Kimi Raikkonen earlier in the session.
Ferrari driver Massa had qualified alongside team-mate Fernando Alonso in sixth place.
He had been on a slow lap in Q2 when Webber came up behind him in the final sector.
Massa felt he had done enough to stay out of the way by clinging to the inside line.
"I was pushing on the inside of the corner and trying not to create a battle with him," he said.
Webber had suspected that Massa had not been informed of his presence.
"It's disappointing. Felipe doesn't do that on purpose, maybe the radio communication wasn't good for his car," said Webber.
"It is a frustrating thing for any of us top guys because we're always generally very good with each other."
The Red Bull driver was only eighth fastest in Q3, saying his rear tyres were worn out before the end of his flying lap.
"I lost the rears, had no rear tyre left. We didn't expect that to happen, but it did," Webber said.
"I bled a lot of lap time from Turn 9 to the start/finish, and then you're losing rows on the grid unfortunately as it's that type of qualifying."
The Gutierrez/Raikkonen incident occurred in the final corners during Q2.
Gutierrez had originally been 16th on the grid.
- Sports & Recreation
- Esteban Gutierrez
- Kimi Raikkonen
- Fernando Alonso