"He didn't test in Barcelona [ Images ] last week because he wanted a bit more time and asked Williams if he could rest," the Australian's partner and manager Ann Neal said on Tuesday.
"But he's fine now, he's been doing a lot of fitness over the weekend."
Neal said Webber, who joined the BMW-powered Williams Formula One team from Jaguar at the end of last year, had picked up the injury in pre-season testing in Spain.
"It was basically a consequence of not warming up properly," she said.
Webber had tested in Valencia in February and did an installation lap without performing his usual warm-up exercises before going out in the car.
Instead of getting out after that one lap to allow mechanics to tweak the settings, the driver was asked to stay in while they worked before carrying on.
"We think the cartilage was damaged then," said Neal. "He then went to test in Barcelona and the actual rib fractured there. But he didn't have any [medical] tests or anything because he was so busy."
Webber then went to hospital while visiting his parents near Canberra on the Wednesday before the March 6 Grand Prix in Melbourne [ Images ].
"He told Gary [Hartstein], the FIA doctor and he gave Mark a couple of injections before the race," said Neal. "He [Webber] didn't want to make a fuss.
"There was never any case of him missing Australia [ Images ], it's not that demanding a circuit, but the big concern was Malaysia," she added.
Webber, very much the home hero for the Melbourne race as the only Australian driver and the first in years with a real chance of winning before his home crowd, finished fifth after qualifying third.
The Malaysian Grand Prix is the most physically demanding race on the calendar with extreme temperatures and high humidity.
Webber's injury was unknown at the time of either race and emerged after McLaren's [ Images ] Juan Pablo Montoya [ Images ] sustained a hairline fracture on his shoulder while playing tennis at the weekend.
McLaren are expected to announce on Thursday whether the Colombian can race or not. Spaniard Pedro de la Rosa, the team's test driver who normally takes part in Friday practice, is standing by.