Tonev, on loan from Aston Villa, had been charged by the SFA following an incident involving Aberdeen defender Shay Logan during a Scottish Premiership match last month.
The Bulgarian was ordered to appear before the SFA’s judicial panel, which ruled he had committed “excessive misconduct by the use of offensive, insulting and abusive language of a racist nature”.
However, Scottish champions Celtic insist they are backing their player’s claims of innocence and plan to appeal.
A club spokesperson said: “Racism has no place in football and as a club for all people, Celtic absolutely abhors racism of any kind.
“This was a very unfortunate case, but the club has accepted Aleksandar’s explanation that he did not say the words that were alleged to have been said and that he is not a racist.
“We are, therefore, very disappointed by the outcome today and can confirm that Aleksandar will be appealing this decision.”
Speaking at the club’s Lennoxtown training complex before the verdict was announced, Celtic manager Ronny Deila backed Tonev.
“I have spoken to him. He said it was not true and I believe him,” Deila said.
“Of course we don’t want racism at Celtic — that is the total opposite as what we want to be as a club. That is not acceptable.”
A spokesman for Tonev’s parent club Aston Villa added: “The position of the club is that racism or any other form of discrimination is abhorrent and has no place in football.
“The club is reviewing the report and decision of the Scottish Football Association and will make no further comment while an ongoing process remains in place.”
Former CSKA Sofia and Lech Poznan star Tonev was making his belated Celtic debut after arriving at Parkhead in the close-season with a groin injury, when the alleged incident took place.
Logan immediately spoke to referee Bobby Madden and skipper Mark Reynolds before informing manager Derek McInnes.
Fourth official Crawford Allan and Celtic were also made aware of the allegation by the Dons management team.