Jackson's horse has won all five of her starts this year, but he said Rachel Alexandra deserved a rest.
"We know the media and many fans would have liked to see her run in the Belmont Stakes and we feel the same," Jackson said in a statement released at Belmont Park. "But all of us sincerely interested in the horse must agree that we only want to see her run when it is best for her.
"While she is in great shape, having strong works, and recovering well from her amazing performances, we feel Rachel deserves a well-earned vacation."
Without Rachel Alexandra competing in the third leg of the Triple Crown, jockey Calvin Borel is free to ride Kentucky Derby winner Mine That Bird at the Belmont -- if he is offered the job.
Borel brought Mine That Bird from last place to a driving finish as a 50-1 shot at the Kentucky Derby, and then switched to Rachel Alexandra at the Preakness.
Mine That Bird came close to catching the filly at the Preakness, but finished second under the ride of Mike Smith.
Smith has another commitment and will not be available for the Belmont. If Borel rides Mine That Bird and wins the Belmont, he would become the first jockey to win all three Triple Crown races in one year aboard two different horses.
Notable deaths of 2014 [PHOTOS]