The promising youngster, 19, who has been linked with a move back to the Premier League with Manchester United, was struck by the white object after he provided the pass for Mario Gotze to head home in the 14th minute.
He slid a stylish ball through for Gotze to nod in the opener at the Westfalenstadion.
Gotze ran to the stands to celebrate and it was when he was joined by his teammates, that Sancho was hit on the right-hand side of his face.
The former Man City youth player needed treatment from medical staff before he was able to return to the action.
His pass for Gotze was his 14th assist in the Bundesliga this season.
It is the most by an English player in one of Europe’s top five leagues since Frank Lampard notched up 14 for Chelsea in the 2009/10 campaign.
His blistering form has caught the attention of Europe’s top clubs and he has four England caps to his name so far.
Man Utd have been linked to him as part of their summer rebuilding plan while his performances have also pricked the ears of Real Madrid who are also ready to spend big after a disappointing season.
Dortmund though are reluctant to allow their prized asset to go.
Gotze’s goal was not to be enough for Dortmund as Schalke turned the game around to win 2-1 on Saturday.