Aberdeen lodged an official complaint to the SFA after Logan told referee Bobby Madden that the Celtic winger had made a racist comment to him during Saturday's Scottish Premiership encounter at Parkhead.
Tonev, who was making his debut for the Glasgow side after signing on loan from Aston Villa in the transfer window, has denied the accusations.
However, the SFA have launched an inquiry into the claims.
"[Aberdeen] confirms it has been contacted by the SFA regarding the alleged racist comment during the SPFL Premiership game with Celtic FC on Saturday 13 September 2014," a statement on Aberdeen's official website read.
"The club will cooperate fully with this investigation. As an employer we support unconditionally any employee who is the subject of any form of abuse and as such believe it is appropriate to allow the SFA the time necessary to carry out a full investigation.
"Consequently, no club official or employee will be making any further comment while the matter is under investigation by the national association."
