Lee was involved in an altercation with Hull defender Alex Bruce at the final whistle of Saturday's fixture, which led to Bruce being dismissed by Howard Webb.
But neither Webb or his officials saw the full incident, and following a review of video evidence, a retrospective charge has been made against the Irishman.
The club and the player have immediately accepted the charge which rules him out of upcoming matches against Crystal Palace, Blackpool and Sheffield Wednesday, and have also confirmed he will face internal disciplinary action.
"Simon Grayson didn't see the incident on Saturday, but he said in his post-match press conference that if Alan had done something wrong he would be punished and this has subsequently happened," chief executive Nigel Clibbens told the club's official website.
"To lose Alan at this time, with three big fixtures coming up, is disappointing and avoidable. The incident at the end of the game was wholly unnecessary, as the game was over."
Lee added: "I raised my arm to protect myself and get past Alex as we came towards each other and he moved across me in an attempt to block my run. There was no intent on my part, but I caught Alex and he then reacted as a result.
"I am a whole-hearted, genuine player and I give my all every second I'm on the pitch. There has been some really harsh, personal criticism in the aftermath of the game, but I fully understand that I have to accept the FA's perception of events.
"I would like to apologise to my team-mates that I won't be available for the next three games and I will look to put things right in the future."