Red Bull broke the overnight curfew at Hockenheim to investigate a problem that had been detected in the gearbox.
It was found that the issue could not be resolved, therefore Red Bull opted to change the box, which will trigger the five-place penalty. Gearboxes are required to last for five events between changes.
Webber is the second driver to run into gearbox trouble this weekend as Mercedes driver Nico Rosberg will also be penalised. Lotus's Romain Grosjean is also carrying the same penalty for a post-Silverstone gearbox change.
Regulations introduced last year prevent teams from being in the circuit for a six-hour period overnight between. At Hockenheim on Saturday morning, this ran from two o'clock until eight o'clock, but Red Bull needed the time to analyse the gearbox.
This is the first time that Red Bull has broken the curfew this season. As each team has four exemptions, no action will be taken.
At Silverstone two weeks ago, McLaren, Caterham and Marussia also broke the curfew.