The Newcastle United midfielder was sent off in yesterday's 0-0 draw at the Cardiff City Stadium.
Hayden, sent on for the second half, was dismissed for a challenge on Josh Murphy which manager Rafa Benitez described as "unnecessary".
The 23-year-old – who had asked to leave the club this summer for "family reasons" – will miss the club's next three games through suspension.
Hayden issued an apology on Twitter after the game.
He tweeted: "Have to apologise to everyone for today, was a needless tackle and one that was stupid from me in that circumstance in the game.
"Will learn from it for sure and will be doing my upmost to repair my mistake today, for my team-mates, manager and staff and fans in the future."
Benitez had revealed before the game that unsettled Hayden was “not OK” with his decision to block a summer move.
Hayden, left out against Tottenham Hotspur last weekend, came off the bench after right-back Javier Manquillo was forced off by an injury.
“It’s difficult to say (if his personal issues affected him),” said Benitez. “It’s not his position, but his tackle was unnecessary. Hopefully, he will learn for the future and will be a better player for it.”
Hayden told the club he wanted to be closer to his infant daughter. However, Benitez turned down Hayden’s request for a move.
“I have been talking to him, and I will try to help as much as I can, but he has to stay and he has to fight for his position,” said Benitez.
“He’s an important player for us. I’ve had this conversation with him before, maybe one month ago or even more, and we decided that he’ll stay.
“Is he OK with that? No, not really. At the moment, he’s still thinking that ‘for me and my family, it will be better to go’, but we’re professionals and we have to do what we have to do at the moment and facilitate the situation as much as we can.”