The ban stems from allegations that Osmajic made racist comments to Burnley's Hannibal Mejbri during a Sky Bet Championship match last season in February.
An independent regulatory commission found the allegations proven on a “Balance of Probabilities”, despite Osmajic consistently denying the charges.
Preston North End expressed “extreme disappointment” with the FA's decision, reaffirming their support for Osmajic and their commitment to anti-discrimination policies.
Alongside the suspension, Osmajic was fined £21,000 and mandated to attend an education course.