The Danish rider was quickly back on his bike and paced back to the peloton by his Astana teammates, but had visible cuts to his right side, including his right elbow and the right side of his face.
The fall involved several riders from Astana, with others from Bahrain-Merida and Jumbo-Visma also involved.
A later update by the Astana team on Saturday confirmed that, following an x-ray and scan, Fuglsang had escaped with no fractures, but that he had "abrasions on his knee, shoulder, and elbow" and was given four stitches for the cut above his eye.
"A rider crashed in front of me at the moment we were going to the front of the peloton to stay out of trouble," Fuglsang said. "It was impossible to avoid him, and so I crashed.
"It's not the way you want to start the Tour. I'm happy that there were no fractures, so I'm able to continue the race. We'll see how it goes tomorrow," he said, with the race continuing on Sunday with a team time trial.