"We simply cannot justify the time and money it will take to continue... beyond 2013," chief executive Eugene Arocca said.
Webber raced in the series for two years in the mid-1990s, finishing fourth in his second year and securing the sponsorship that would enable him to move to Europe to further his dreams of driving in Formula One.
Daniel Ricciardo, the Toro Rosso driver who hopes to take over from Webber at Red Bull next year, also made a brief cameo in the series and many of the champions in the popular national V8 series have also featured.
The state Formula Ford Championships - Ricciardo made his senior racing debut in the Western Australian version in 2005 - would continue, Arocca said.
"It is expensive for everyone competing in the national competition and we feel there is a better, more affordable, more sustainable way of showcasing Formula Ford racing nationally," he added.