The 20-year-old frontman was sent off in Saturday's 3-0 Tannadice defeat after launching into a late tackle on Arabs midfielder Willo Flood.
Referee Euan Norris decided the challenge amounted to serious foul play and produced a straight card.
His report has now been received by Scottish Football Association officials at Hampden, who have confirmed to the club that a two-match punishment will be imposed.
The suspension is immediate and means Naismith will miss Rangers' fixtures with Queen's Park this weekend and Clyde at Broadwood on February 16.
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