Bild reports defender Marc Bartra was the individual injured after the incident and was taken to hospital, but is said to be ok.
Dortmund reiterated the rest of the players are safe and there was no danger inside or around the stadium.
The incident reportedly took place around six miles away from the Westfalenstadion in Hochsten, as the team left their hotel.
Fans in the stadium waited for an announcement as Monaco fans inside the Westfalenstadion showed their support for the home side.
The encounter has been rescheduled for Wednesday night with a 5:45pm kick-off.