The 22-year-old remains in a critical condition in hospital after suffering life-threatening injuries in a car crash on Friday.
Hoffenheim general manager Andreas Muller said: "This is the most difficult situation the team has ever been in.
"We would have been able to call the game off, but the team decided unanimously to play. We want our positive energy to be transmitted to the lad. We want to fight for Boris because he is also a fighter.
"After receiving that message (from Vukcevic's parents), the team and the club decided to play."