The Danish rider crashed along with Team Sunweb's Cees Bol with approximately 27km left in the stage.
Fuglsang was ninth place in the GC, 5:27 behind race leader Julian Alaphilippe (Deceuninck-Quickstep). The 34-year-old was a pre-race favourite after winning the Criterium du Dauphine.
The team later confirmed that Fuglsang did not break any bones but that he was in too much pain to continue.
"I'm really disappointed about leaving the Tour de France this way, but there was too much pain to continue," Fuglsang said in a team press release. "Somebody crashed in front of me and there was no way to avoid it, so I crashed over my handlebar. My hand directly swelled up and I could barely stand on my feet, I directly knew my Tour would finish here.
"I was very motivated for the final week and I was ready to battle for a higher position in the GC. That this has to be the way of missing out on this battle, is just very disappointing. Now all the focus will be on recovering, both physically as mentally, because the Tour was a big goal after my wins in Liége and the Dauphiné."