A number of arrests were made amid trouble from both sets of fans, during a tense day on which Schalke dealt a severe blow to their rivals' Bundesliga title bid.
TV footage showed Sancho, 19, being hit by a projectile as he celebrated Dortmund's opening goal with teammates just in front of the Schalke fan section. He was briefly taken off the pitch for treatment, but returned to play the rest of the game.
In a statement on Saturday, police said they had opened criminal proceedings on the basis of aggravated battery.
The Ruhr derby is generally subjected to a high level of security, with hundreds of police officers deployed to keep opposing fan groups separated both at the game and on their way to and from the stadium.
Saturday's game in Dortmund was nonetheless overshadowed by a handful of ugly incidents, involving what police called an “unteachable and violent minority” of fans.
Before the game, a group of Schalke fans attempted to storm the turnstiles, leading to delays in security checks. At full time a group of Dortmund fans attempted to break their way into the away block, but were beaten back by officers. The police also confirmed the use of pepper spray in a confrontation at a local metro station.
In total, police confirmed they had taken 13 people into custody and filed charges against 36 people, both for assault and breaches of the Explosives Act.
The police statement said that the use of flares in the home block towards the end of the game had left six people injured, two of which were hospitalised. Schalke fans also set off flares at kick-off, unleashing a cloud of blue smoke across the field.
They later held up a tasteless banner demanding the release of Sergei Wenergold, the man who was jailed for attempted murder after a bomb attack on the Dortmund team bus in 2017.
Former Dortmund player Marc Bartra, who was injured in the 2017 attack, condemned the banner on Twitter, saying that it was “unacceptable” and “sad”.
“Rivalry in football is one thing, it is quite another to demand freedom for someone who played with the lives of 28 people,” wrote the Spanish defender, who now plays in Seville for Real Betis.