The South American trio will not feature in Wednesday's King's Cup round-of-32 second leg against Hercules at the Nou Camp after being released for the Christmas holidays early by coach Luis Enrique.
All three started Sunday's 4-1 home win over city rivals Espanyol, a game in which Suarez scored twice and Messi once as the Catalans climbed to second in La Liga.
They are three points behind Real Madrid, who have a game in hand after their participation in the Club World Cup.
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"The front three have never played the first round of the cup and I believe it is necessary that they begin their vacations," Barca coach Luis Enrique told the club website.
Barcelona defender Gerard Pique is the only other player in the team to have been given permission to begin the holidays early.
The rest of the squad will be available for selection on Wednesday before enjoying seven or eight days off to be with their families, Luis Enrique said.
Messi scored his 12th league goal of the season on Sunday to join Suarez at the top of the La Liga scoring charts.
The Argentine also produced a mazy run in the build-up to Suarez's second goal.
"Leo's play is out of a Playstation, of a unique player," Suarez told Marca, before offering his opinion about Cristiano Ronaldo winning the Ballon d'Or ahead of Messi.
"Many people already know that Leo Messi is the best in the world," he said. "He does not have to win an award because the people already know he is the best. We must enjoy having him."
Barca defender Javier Mascherano echoed those sentiments.
"Messi is a player who always leaves us speechless," he said.
(Reporting by Adriana Garcia, editing by Ed Osmond)
