The 24-year-old was placed on report by the referee after a tackle on Greg Bird in Friday's 46-10 win over Catalans Dragons at Headingley.
Bird required seven stitches in a wound at the back of his head.
Singleton will not be available for the Rhinos until the game against Huddersfield Giants on 27 April.
In other disciplinary hearings, Hull FC's Jansin Turgut was suspended for two matches and fined £300 after pleading guilty to striking with an elbow or forearm in the match against St Helens.
Salford prop Lama Tasi has been given a one-game ban after submitting an early guilty plea for a dangerous throw on Wakefield's Anthony England.
Leigh Centurions' Gareth Hock pleaded guilty and was fined £300 for a grade A punching offence.
St Helens' Alex Walmsley, Widnes' Danny Craven and Huddersfield's Sebastine Ikahihifo have all escaped suspension after they submitted early guilty pleas.
Leeds Rhinos forward Brad Singleton has been banned for six matches and fined £300 after pleading guilty to striking an opponent with his elbow.