His withdrawal was announced first by the Scottish Football Association via their social media channels.
The loss of the Hull City defender follows the news that Christophe Berra has also been forced out of the match in Dortmund on Sunday. Mark Reynolds was called up to replace the former Hearts captain.
Craig Forsyth, Steven Whittaker or Alan Hutton could replace Robertson at left-back, with the 20-year-old focused instead on regaining his fitness for a league match with West Ham United. He wrote on Twitter: "Gutted to be injured. Good luck to all the boys."