No fractures for MotoGP star Bagnaia after Catalunya crash
Sunday's race was red-flagged after Bastianini's bike slipped at turn one of the opening lap, taking out four other riders, before Bagnaia was launched into the air by a highside on the next turn.
Bagnaia, whose leg was run over by KTM's Brad Binder straight after his crash, was conscious and taken to hospital for treatment.
Both riders were unable to return for the race's restart, with Aprilia's Aleix Espargaro claiming victory.
"Bagnaia has sustained multiple contusions, but further medical checks have shown no fractures. The reigning World Champion will fly to Italy with the team tonight," Ducati said in a statement on social media.
"(Bastianini) suffered a non-displaced fracture of the medial malleolus of the left ankle and a sub-capital fracture of the second metacarpal of his left hand.
"Bastianini will require surgery on his ankle and, to speed up his recovery, he will also undergo surgery on his hand in the following days."
World champion Bagnaia leads Pramac Racing's Jorge Martin by 50 points in the championship standings.
The MotoGP calendar resumes with the San Marino Grand Prix at the Misano circuit next week.