"Tom has fractured his radius in his left forearm," team doctor Stephan Jacolino said. "It's a clean fracture and further examinations have shown no additional fracture of the wrist joint, which is good news.
"Tom will have further tests in the Netherlands to determine if surgery is required to stabilise the fracture and to make a treatment plan."
The Giant-Alpecin rider, one of the main favourites for the August 10 Olympic event, fell with about 62km left in the 146km stage fromAlbertville to Saint-Gervais Mont Blanc, and abandoned the race in tears a couple of kilometres further on.
"It's a huge setback. After the crash I instantly knew it was bad news. Luckily it is a clean fracture," Dumoulin said.
"As a precaution I have a cast but I can't ride a bike with it. If I need to keep this for two weeks, then my participation in Rio will be difficult.
"Tomorrow I go back to the Netherlands and we can see how we proceed. I really hope I will be ready for the Olympics. At the moment there is too little information to say anything more about that objective."
Dumoulin won two stages in this year's Tour, a summit finish in Arcalis, Andorra, and the first time trial. He was second in Thursday's mountain time trial behind overall leader Chris Froome.