The Football Association charged Osmajic in March for an alleged racist remark made against Tunisian midfielder Mejbri during their 0–0 Championship draw at Deepdale in February.
The FA said that an independent Regulatory Commission found that Montenegrin forward Osmajic's actions constituted an 'aggravated breach', as defined in FA Rule E3.2, as the words included a reference to colour and/or race. Osmajic had denied the charge.
Preston said in a statement that they were "extremely disappointed" with the decision.
"Milutin has always pleaded his innocence and continues to do so. We continue to be fully supportive of our player," the club added.
The 26-year-old has also been fined 21,000 pounds ($28,184) and has been ordered to complete an education course.