Ducati said the Italian suffered heavy bruising when he fell at the Arrabiata-2 corner of the Mugello circuit, which hosts the Italian Grand Prix at the end of May, on the last day of the private test.
Doctors later diagnosed a dislocated left shoulder.
"Over the next three days Iannone will follow treatment agreed with his specialist, with the aim of lining up for the start of the French GP at Le Mans," the team said on their website.
Iannone is fifth in the standings, just six points adrift of Honda's world champion Marc Marquez, after a promising first four races of the season. He finished third, his first MotoGP podium, in the Qatar opener.
(Reporting by Alan Baldwin, editing by Toby Davis)