Matondo, was pictured in a Dortmund jersey bearing the name of England winger Jadon Sancho.
"I made it very clear to Rabbi Matondo on the phone what I think of such an ill-considered action," Schalke sports director Jochen Schneider told AFP subsidiary SID on Tuesday.
"He is only 19 years old, but that still shouldn't have happened.
"We clearly told him that he had to show the right reaction to his misconduct both on and off the pitch."
Just 30 kilometres (19 miles) separates Gelsenkirchen-based Schalke and Dortmund, but there is no love lost between the sides in the Ruhr Valley, the industrial heartland of western Germany.
The post of Matondo in a Dortmund top was quickly taken down after a flurry of angry comments from Schalke fans, including "There's the door!" and "Rabbi Matondo wearing a BVB jersey in the gym. You couldn't make it up!"
Several Royal Blues followers said they hoped Matondo was wearing the shirt for a bet.
However, one furious supporter wrote: "When it comes to football, it's just a no-go for me and I don't care whether it was a bet or if he likes the colour yellow."
Despite their clubs' deep rivalry, Matondo is friends with Dortmund star Sancho.
Matondo joined Schalke in January 2019 for around 10 million euros ($11 million) from Manchester City, where he had played in the club's academy alongside Sancho, 20, who signed for Dortmund in August 2017.
While Sancho netted 17 goals and created as many assists as Dortmund finished Bundesliga runners-up to champions Bayern Munich in 2019/20, struggling Schalke and Matondo had a season to forget.
He managed two goals in 20 matches as his side went winless in their last 17 games to finish 12th in the league table having been third in December.