Jeffers was shown a straight red card in the 37th minute for headbutting and punching Vale skipper Tommy Fraser before second-half goals from Kris Taylor and Rob Taylor knocked the Owls out of the competition.
Former Arsenal striker Jeffers subsequently apologised for his dismissal but Brian Laws has slammed the striker, handed him a maximum club fine and put him on the transfer list.
"His conduct was totally unacceptable and something this football club will not tolerate from any player," Laws told the club's official website.
"We have therefore enforced the heaviest punishment available to the club with immediate effect and transfer-listed the player.
"The kind of behaviour enacted on Tuesday night is completely unacceptable and does not represent what Sheffield Wednesday stands for and clearly sets a bad example for the game of football."
Earlier Jeffers had told Sky Sports News: "I did not sleep well and I wanted to make an apology.
"There were a few incidents before and then bit of a coming together between us and a clash of heads.
"The manager did not say to much to me, he was just disappointed to have lost the game. I've let the club down, the players, the manager and the fans and I just wanted to say sorry."
Asked if he would contact Fraser to apologise personally, Jeffers added: "I'm not sure yet. I expect I'll try and get the lad's number but I think he will understand why it happened."