Osmajic bit Beck during the closing stages of a goalless Championship draw between the Lancashire rivals at Deepdale on September 22.
The Montenegro striker became embroiled in the clash with Beck moments after the Blackburn player was sent off for kicking Preston's Duane Holmes in the second-tier fixture.
Blackburn boss John Eustace said in his post-match press conference: "Beck's got a big bite mark on the back of his neck. He's shown all the lads. He's a little bit quiet, a little bit shook up."
As well as the lengthy ban, Osmajic - who admitted the charge of violent conduct - has been fined £15,000 for his behaviour.
"The forward admitted that he committed an act of violent conduct around the 87th minute by biting an opponent," the Football Association said on Friday.
Former Uruguay forward Luis Suarez, now of Inter Miami, has served a number of bans during his career for biting incidents, including a 10-game suspension while playing for Liverpool.
