The club's five-strong ethics committee, in a statement late Tuesday, said Toennies had "violated the ban on discrimination contained in the club's statutes" after a lengthy meeting in which Toennies had to explain himself.
The club said Toennies had decided to step down as a member and chair of supervisory board for three months.
"He admitted the violation at the meeting on Tuesday and expressed his regret once again," said the panel in a statement.
However, the body dismissed the accusation of racism as "unfounded" and consequently spared him the heavier sanction of firing him.
The 63-year-old has been sharply criticised for saying more power stations should be built in Africa, "then Africans would stop felling trees and producing children when it gets dark".
The billionaire businessman, who employs 16,500 people and has assets estimated by Forbes at around 2.2 billion euros ($2.5 billion), made the remark at a forum in Paderborn last Thursday while criticising tax increases to fight climate change.
On social media, numerous Schalke fans and former players demanded his resignation as chairman of the club's supervisory board, while senior figures in German football and politics have condemned his comment.
- 'Devastating' -
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Politician Dagmar Freitag, the chairman of the sports committee in Germany's parliament, the Bundestag, criticised the finding of Schalke's ethics committee.
"If I had pigeonholed an entire continent and its population, then it would be racism rather than 'just' discrimination, as far as I am concerned," she told broadcaster NRD.
"Such lapses are a break in what is taboo, without scruples, and their effect on society is -- especially in these times -- devastating."
Toennies had apologised for his "inappropriate" words on Sunday, insisting he backs Schalke's values against "racism, discrimination and exclusion".
Justice Minister Christine Lambrecht had previously called on the German Football Association (DFB) to "deal" with Toennies.
"Racism must be loudly and clearly contradicted" at every opportunity, the politician told the Funke media group.
"Nowhere is integration as successful and quick to work as in sport - that must not be put at risk."
Cacau, the Brazil-born former Germany star who heads the DFB's integration committee, was also stunned by Toennies comment.
"The longer I think about it, the more unimaginable it becomes that a man of his position and experience speaks so... disparagingly about the population of an entire continent," said the 38-year-old.
Former Schalke forward Gerald Asamoah, Germany's first black international, said he was left "somewhat speechless" by Toennies remark.
"I have been working with Clemens Toennies for a long time, and we have been close friends for a long time," wrote the 40-year-old Asamoah on Instagram.
"He never behaved in a racist manner towards me.
"I was very surprised, shocked and injured by his statement."
Toennies comments have become a distraction for Schalke, under new head coach David Wagner, who start their league season at Borussia Moenchengladbach on August 17.