Thomas was fastest to remount, finishing 5:56 down on stage winner and race leader Maximilian Schachmann (Bora-Hansgrohe), while Kwiatkowski took longer to get rolling, coming across with teammate Kenny Elissonde 9:38 down.
Team Sky doctor Iñigo Sarriegui confirmed that Castroviejo was taken to hospital.
"Jonathan is having a scan to check that there is no major injury, but I suspect he has fractured his right clavicle. The scan will show if there are any other associated injuries. We will know more after that," Sarriegui said.
Gabriel Rasch, Team Sky's directeur sportif for the race, said both Thomas and Kwiatkowski fell hard but are OK.
"The last 10k were very open, we knew it was going to be like that and so did everyone else, so everyone wanted to be at the front in case the wind had an impact," Rasch explained. "The road narrowed a lot with about 5k to go and that was another reason to be towards the front. I don't think there was any special reason for the crash.
"The road was three or four lanes wide and the guys were all together and ready to move up before that narrower section with 5k to go. That's why they all went down together. I don't think there was anything wrong with their position. [Julian] Alaphilippe also went down because he was in the same position, it was just unlucky."
Get The Leadout Newsletter
The latest race content, interviews, features, reviews and expert buying guides, direct to your inbox!
Rasch expects that Thomas and Kwiatkowski will be able to continue the race.
"For sure they will both start tomorrow. The doctor see them every night and every morning so they'll get checked over before then."
With Thomas and Kwiatkowski out of the GC picture, Team Sky's best-placed rider is now Diego Rosa, who is 2:32 down on Schachmann.
