The pair were cited for "aggressive and inappropriate actions" by MLB vice president Bob Watson and started serving the penalties immediately, a day after they tangled.
Yankees utilityman Shelley Duncan was suspended for three games and appealed, delaying the start of any discipline.
Toronto manager Cito Gaston said Carlson was fined $3,000 and that Blue Jays catcher Rod Barajas was docked $1,000. Posada was fined $2,500, and Yankees hitting coach Kevin Long and pitcher Edwar Ramirez also were fined.
Posada and Carlson were initially given four-game suspensions that were reduced to three when they agreed not to appeal.
The New York Daily News first reported the Posada penalty.
After a pair of Toronto players were hit by pitches Tuesday night, Carlson threw a fastball behind Posada in the eighth inning of the Blue Jays' 10-4 win. Moments later, Posada bumped Carlson after scoring a run, and the dugouts and bullpens emptied.
Even before the suspension, Posada was not in the starting lineup for the series finale because of a stiff neck, which Yankees manager Joe Girardi said was sustained in the fight.
"That is part of baseball, but that's a part of baseball that I don't like," Girardi said. "No pun intended, but it's a black eye for baseball to me whenever there's a fight or an incident like that because, you know, someone can really get hurt and you can jeopardize someone's career. .. They've been protecting players for years. It's an ugly part of the game, but I think it's important for a team standpoint that you know you have each other's back. That's very important, and that will never change."
Girardi said he did not get hit by a fist from Toronto infielder John McDonald as he lunged into the scrum. McDonald and Girardi spoke about it before batting practice.
"He was quite disturbed that his name was mentioned in that sort of situation. He's a peacemaker," Girardi said. "I got elbowed accidentally by one of my own players."
Said McDonald: "I just wanted to let him know that the only reason why I was out on the field was to help make sure nobody got hurt."
Posada was not available in the clubhouse before Wednesday's game and Duncan said he had not yet been informed of any discipline.
Gaston understood the penalty against Carlson, who was left with a large red knot on the left side of his forehead.
"I'm not upset with it. It's got to be done," he said. "It's always too many days, but what are you going to do?"
Umpire Jim Joyce said after the fight that Posada's elbow shove of Carlson was "very unsportsmanlike" and a "cheap shot."
"The intensity that we love in Jorgy, sometimes these are the types of things that happen," Girardi said. "But I love his heart. I love his intensity and I wouldn't want to take that away from him."
"I am concerned about Mark because it's happened a couple times and I know he feels extremely bad about it," Girardi said. "Pitchers don't have Nintendo controllers in their pocket."
Melancon has hit four batters this year. He throw a pitch over the head of Boston's Dustin Pedroia on Aug. 6, then hit him.
He said he didn't intend to hit Hill and that he's had a problem with his arm lagging on his two-seam fastball.
"I don't think I've ever walked this many people in my life, let along hit these many people. It's been tough for me to swallow," said Melancon, who has walked 10 in 16 1-3 innings.
Information from The Associated Press was used in this report.