Wilson made the allegations in a letter he released Saturday in which he quit the team and also complained that the coaching staff would "belittle, intimidate and humiliate us."
Leach said during his regular Monday meeting with reporters: "There is no truth about it at all." He described Wilson as a disgruntled player.
Asked if there had been any actions by coaches that could be construed as abuse, Leach replied: "No, no, no. Next question."
Wilson issued a statement on Saturday saying he had quit the team as a protest to "physical, emotional and verbal abuse" by the coaching staff. He did not provide examples and has not been available for comment.
Wilson is WSU's career leader with 3,207 receiving yards, but has been a regular target of criticism from Leach and his assistants since spring drills. More recently he was demoted to backup receiver, although he continued to lead the team in receptions and yards.
Washington State President Elson Floyd on Sunday asked the school's athletic department and the Pac-12 Conference to conduct separate investigations into Wilson's allegations.
"Together, both reports should get to the bottom of the matter," Floyd said in a press release.
Leach said he had no problem with the two investigations, which he expected would "dispel all the falsehoods that surround this.
Wilson was suspended after walking out of a tough conditioning drill on Nov. 4.
"Sixty five people went through that workout, and he left after 15 minutes and nobody went after him," Leach said. "That says more about him than anybody or anything else."
Several players asked if they have witnessed abuse either declined to comment or denied seeing any abuse.
"Staying away from all that is the smart thing to do," said quarterback Jeff Tuel, a close friend of Wilson, on Monday.
"I haven't seen any sort of physical abuse at all," center Elliott Bosch said.
Leach was fired from Texas Tech after the 2009 season for an incident in which he was alleged to have ordered a player with a concussion to sit in a storage shed during practice. Leach disputed the allegation and it was not proven. Leach has sued Texas Tech, contending he was fired so the school could avoid a large payment due him at the end of the year.