Dons defender Logan immediately reported the alleged second-half incident 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.
The Scottish FA is awaiting the referee's report which should arrive on Monday.
Celtic did not comment when contacted on the incident.
Bulgaria winger Tonev, 24, was making his belated Celtic debut after arriving in the summer on a one-year loan deal from Aston Villa with a groin injury.
Ronnie Deila's side won the league match 2-1 thanks to goals in either half from Jason Denayer and Kris Commons, to end a run of four games without a victory.