Mejbri complained to the referee after Osmajic made the alleged racist comment during the 0-0 Championship draw between the two sides at Deepdale on February 15th.
Preston said Osmajic strongly denies the allegation.
"It's alleged that the forward acted in an improper manner and/or used abusive and/or insulting words towards an opposing player..." the FA said in a statement announcing the charge.
The FA added it was further alleged that this constituted an "aggravated breach" as it included a reference to colour or race.
Preston acknowledged the charges and added that they would not be making further comment until the case has been concluded.
"Milutin continues to strongly deny the allegations of the use of abusive language with reference to colour and/or race and will provide an official response to the FA charges in due course," the club said in a statement.
The 25-year-old Osmajic has until March 25th to respond.