The German international was replaced by Felipe Santana after limping out of the game at the Etihad Stadium after 74 minutes and Hummels explained the initial diagnosis of the injury.
“It's not broken or cracked,” Hummels told Der Western. “Maybe it's just a pinched nerve. At the moment I could not even play boccia.”
The knock means Hummels will now miss Sunday’s trip to Hannover.
Mario Balotelli’s injury-time penalty was enough to rescue to a point for Roberto Mancini’s side after Marco Reus had put the German Champions ahead just after the hour mark.
The result leaves Dortmund in second place in group D, two points behind leaders Real Madrid and three points above City.