A jury ruled Jur Vrieling of the Netherlands went too hard on the whip, while Belgium's Nicola Philippaerts was disqualified for excessive use of spurs under International Equestrian Federation guidelines.
While the riders are out of the individual competition, they can continue competing for their teams. Vrieling was part of the silver-medal-winning Dutch team in London 2012, when Britain claimed gold.
Jumping is the last of three equestrian competitions in the Olympics.
A leading Dutch dressage rider, Adelinde Cornelissen, earned praise on social media for pulling out of a test on Wednesday because she was worried about her sick horse, even though it had been cleared by a vet for competition.
Host Brazil and Germany were the only countries to emerge without team penalties in the first qualifying show jumping round on Sunday in which the worst of four scores is dropped.
"It is the same feeling as a soccer player when he scores in a final," Brazilian rider Alvaro de Miranda Neto, known as Doda, said of local fans' reception to his clear round.
Riders go on to a second qualifier on Tuesday. Team medals are awarded on Wednesday and individual medals on Friday.
(Reporting by Caroline Stauffer; Editing by Bill Rigby)
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