The action was taken after the allegations emerged on Friday morning.
Cardiff manager Ole Gunnar Solskjaer earlier dismissed any suggestion of involvement by any member of the Cardiff squad.
The Welsh club's chairman Mehmet Dalman has been in contact with the Premier League over the incident. The relegation battle ended in a 3-0 defeat for the Bluebirds.
It is understood that Premier League officials have requested information on Cardiff's case.
It is thought the person sacked has been dismissed for gross misconduct following an internal enquiry at the club.
It is understood Cardiff have complained to the Premier League about the circumstances surrounding the alleged leaking of their team ahead of last Saturday's game.
Palace sporting director Iain Moody worked for Cardiff until earlier this season. He took up a post at Palace last November.
It has been reported that Cardiff believe Moody might have used his contacts at the Welsh club, or close to Cardiff, to find out which players would start against Palace.
Moody, though, has rebutted the allegations, sayng : "That is incredibly, extraordinarily untrue. That is untrue, completely untrue."
Cardiff are currently six points adrift of Premier League safety, lying 19th ahead of Saturday's trip to Southampton with just five games left.
Asked about the allegations at his pre-Southampton press conference on Friday, Solskjaer said: "My week has been on how we can give ourselves the best chance against Southampton.
"I think I have seen every one of my players and I don't doubt anyone's pride, honesty, loyalty, integrity, professionalism. They have all been fantastic this week.
"I have built my life on loyalty and honesty, and those are the values I get from my mum and dad. But in football you need to stick together and learn together, and this week has proved that more than anything.
"I have just said I have no reason to doubt any of my player's professionalism, or honesty, integrity or loyalty.
"I have said what I have said, and the rest will come from Mehmet.
"I am not talking about Crystal Palace. We've got Southampton, and that's my job to get ready for that game. When you are in a football club, you stick together. That's the key."
Cardiff captain Steven Caulker added: "We have got to focus on the situation we are in at the moment. Our focus as players is to put things right from last week, really."
It is understood any alleged leak to Palace has not come from within the Cardiff squad.
However, Caulker added: "To be honest with you, there have been problems like that all season where certain things have been leaked.
"For me, it is frustrating. We need to focus on getting things right on the pitch, not what's going on off the pitch.
"I will be telling the boys that we need to get performances in and get results, not concern ourselves with off-the-field issues.
"A lot of stuff has been going on off the pitch all season, and that has been highlighted in the press. It is important we all ignore all that stuff. Our performances have not been up to scratch of late.
"As far as the boys are concerned, we back ourselves. We've had the support of the fans all season, we've had the support of both managers we've worked under. I find it hard to see where it could be coming from.
"You have a bit of banter with your ex team-mates and friends in football. Until the Premier League has investigated it and got to the bottom of it, I certainly won't be pointing any fingers."
Cardiff's performance against Palace suggested that the game might be up in terms of avoiding a quickfire Championship return, but Solskjaer has no intention of throwing in the towel.
"I am up for a fight, that's for sure," he said.
"There is absolutely nothing wrong with the atmosphere. We have had a very good week again. They are a great bunch of lads, and they have picked themselves up from the hurt of what happened last week."