The 25-year-old sustained a blow to the chin during the first half of the clash in Niigata, but remained on the field before being withdrawn in the final minute.
A statement on Dortmund's official website on Saturday revealed that Kagawa may have a slight concussion but that the problem "does not appear to be serious".
After the match, Kagawa complained of dizziness and was taken to hospital.
Japan coach Javier Aguirre has subsequently agreed to let the midfielder return to Germany, meaning he will miss Tuesday's friendly against Brazil in Singapore.
As soon as Kagawa is given the all-clear by Dortmund's medical staff he will return to training, where he will join Henrikh Mkhitaryan.
The Armenia international is back in full training after recovering from a foot injury, while Marco Reus (ankle) and Ilkay Gundogan (back) are also pushing for a return to the fold ahead of next weekend's trip to Cologne in the Bundesliga.
