Arians was attempting to move Adams, who was trying to pull a player out of a pile after a muffed punt by Jalen Reagor, which would have drawn a penalty. He can be seen slapping Adams' helmet hard with an open hand and then elbowing him.
Adams wasn't penalized on the play.
"I'll appeal it," Arians said Wednesday. "It ain't got nothing to do with the game, so we're good."
A source told ESPN that the note to Arians stated that he displayed "conduct directed towards your players that fell below standards expected of an NFL head coach."
Last month, then-Jacksonville Jaguars coach Urban Meyer came under increased scrutiny when former kicker Josh Lambo told the Tampa Bay Times that Meyer had kicked him during warm-ups at a practice. Meyer was fired the next day, but it was for a litany of issues.
Arians was asked Monday whether he regretted making physical contact with a player.
"No," Arians said. "I've seen enough dumb. You can't pull guys out of a pile. We just got a big play, great field position, and he's trying to pull a guy out of a pile and I was trying to knock him off that guy so he didn't get a penalty."