Rossi, whose title hopes are effectively over, had surgery on his broken right leg last week and left hospital on Saturday.
Doctors have said the Italian, fourth in the overall standings and 26 points behind leading compatriot Andrea Dovizioso, will need 30-40 days' rest.
Six MotoGP races remain and the Italian looks set to miss the next one after Misano, at Spain's Aragon circuit on Sept. 24, as well although he has vowed to return as soon as possible.
In 2010, Rossi broke his right leg in practice for the Italian Grand Prix and took six weeks to return.
(Reporting by Alan Baldwin in London, Editing by Ken Ferris)
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