The Power forward will sit out Saturday night's blockbuster at Adelaide Oval, telling the club on Thursday he was mentally in no position to play.
"With all the stress from this week, I feel it's best for me and the team that I take a break," Rioli said via a statement from Port.
"I again acknowledge that my actions after last weekend's game against the Bulldogs were totally unacceptable."
The 29-year-old initially escaped sanction from the AFL despite sending an intimidating message about Bailey Dale to one of the Western Bulldogs defender's teammates, the day after a heated match in Ballarat on Saturday.
But the AFL decided to probe further after reports emerged of  two verbal threats allegedly made by Rioli to a Geelong and an Essendon player.
Rioli and Port football boss Chris Davies met with AFL officials ahead of the Power's training session on Wednesday.
"I apologised to Bailey Dale on Monday and I want to publicly apologise again for the stress my actions have caused," Rioli said.
"I say things from time to time on the footy field in the heat of the moment that I wish I didn't and I'm continuing to work with the club on managing this moving forward.
"It's not in my true nature or character to say those things and I apologise for any distress I cause to individuals or their families.
"I want to thank the Port Adelaide Football Club and all of my teammates and coaches for their support."
The AFL hasn't commented on the situation since releasing a brief statement on Monday: "while confirming it will take no further action to that undertaken by the clubs and players, it has reminded both clubs to ensure any communications remain respectful."
On Wednesday, Port president David Koch said the club was "incredibly angry" about the situation.
"We've talked pretty sternly to Willie about it and said it's just not on," Koch told 5AA Radio.
"I'm making absolutely no excuse for Willie's private message after the game.
"But you can't mix on-field and off-field comments or it will lead to places people don't want to go."